diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index b8e9efa45..d1d4f3345 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -1647,6 +1647,20 @@ class binary_writer
         return 'D';  // float 64
     }
 
+    /*!
+    @brief checks whether a JSON number fits into @a TargetType
+    @param[in] el a JSON number of either the signed or unsigned integer kind
+    @return whether @a el's value can be represented by @a TargetType without
+            wrapping, regardless of which of the two kinds it is stored as
+    */
+    template<typename TargetType>
+    static bool bjdata_ndarray_value_in_range(const BasicJsonType& el)
+    {
+        return el.is_number_unsigned()
+               ? value_in_range_of<TargetType>(el.template get<std::uint64_t>())
+               : value_in_range_of<TargetType>(el.template get<std::int64_t>());
+    }
+
     /*!
     @return false if the object is successfully converted to a bjdata ndarray, true if the type or size is invalid
     */
@@ -1731,6 +1745,60 @@ class binary_writer
             }
         }
 
+        // every element is cast to the (possibly narrower) C++ type matching
+        // dtype below; a value that does not fit that type would silently
+        // wrap (integers) or overflow to infinity (the "single" precision
+        // float) instead of being reported, so such an object falls back to
+        // a plain object encoding as well
+        for (const auto& el : value.at(key))
+        {
+            bool in_range = true;
+            switch (dtype)
+            {
+                case 'U':
+                case 'C':
+                case 'B':
+                    in_range = bjdata_ndarray_value_in_range<std::uint8_t>(el);
+                    break;
+                case 'i':
+                    in_range = bjdata_ndarray_value_in_range<std::int8_t>(el);
+                    break;
+                case 'u':
+                    in_range = bjdata_ndarray_value_in_range<std::uint16_t>(el);
+                    break;
+                case 'I':
+                    in_range = bjdata_ndarray_value_in_range<std::int16_t>(el);
+                    break;
+                case 'm':
+                    in_range = bjdata_ndarray_value_in_range<std::uint32_t>(el);
+                    break;
+                case 'l':
+                    in_range = bjdata_ndarray_value_in_range<std::int32_t>(el);
+                    break;
+                case 'M':
+                    in_range = bjdata_ndarray_value_in_range<std::uint64_t>(el);
+                    break;
+                case 'L':
+                    in_range = bjdata_ndarray_value_in_range<std::int64_t>(el);
+                    break;
+                case 'd':
+                {
+                    const auto dval = el.template get<double>();
+                    in_range = !std::isfinite(dval) ||
+                               (dval >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                                dval <= static_cast<double>((std::numeric_limits<float>::max)()));
+                    break;
+                }
+                default:
+                    // 'D' (double) already spans the full range of number_float_t
+                    break;
+            }
+            if (!in_range)
+            {
+                return true;
+            }
+        }
+
         oa->write_character('[');
         oa->write_character('$');
         oa->write_character(dtype);
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 31bfb869d..824dad6e1 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -18655,6 +18655,20 @@ class binary_writer
         return 'D';  // float 64
     }
 
+    /*!
+    @brief checks whether a JSON number fits into @a TargetType
+    @param[in] el a JSON number of either the signed or unsigned integer kind
+    @return whether @a el's value can be represented by @a TargetType without
+            wrapping, regardless of which of the two kinds it is stored as
+    */
+    template<typename TargetType>
+    static bool bjdata_ndarray_value_in_range(const BasicJsonType& el)
+    {
+        return el.is_number_unsigned()
+               ? value_in_range_of<TargetType>(el.template get<std::uint64_t>())
+               : value_in_range_of<TargetType>(el.template get<std::int64_t>());
+    }
+
     /*!
     @return false if the object is successfully converted to a bjdata ndarray, true if the type or size is invalid
     */
@@ -18739,6 +18753,60 @@ class binary_writer
             }
         }
 
+        // every element is cast to the (possibly narrower) C++ type matching
+        // dtype below; a value that does not fit that type would silently
+        // wrap (integers) or overflow to infinity (the "single" precision
+        // float) instead of being reported, so such an object falls back to
+        // a plain object encoding as well
+        for (const auto& el : value.at(key))
+        {
+            bool in_range = true;
+            switch (dtype)
+            {
+                case 'U':
+                case 'C':
+                case 'B':
+                    in_range = bjdata_ndarray_value_in_range<std::uint8_t>(el);
+                    break;
+                case 'i':
+                    in_range = bjdata_ndarray_value_in_range<std::int8_t>(el);
+                    break;
+                case 'u':
+                    in_range = bjdata_ndarray_value_in_range<std::uint16_t>(el);
+                    break;
+                case 'I':
+                    in_range = bjdata_ndarray_value_in_range<std::int16_t>(el);
+                    break;
+                case 'm':
+                    in_range = bjdata_ndarray_value_in_range<std::uint32_t>(el);
+                    break;
+                case 'l':
+                    in_range = bjdata_ndarray_value_in_range<std::int32_t>(el);
+                    break;
+                case 'M':
+                    in_range = bjdata_ndarray_value_in_range<std::uint64_t>(el);
+                    break;
+                case 'L':
+                    in_range = bjdata_ndarray_value_in_range<std::int64_t>(el);
+                    break;
+                case 'd':
+                {
+                    const auto dval = el.template get<double>();
+                    in_range = !std::isfinite(dval) ||
+                               (dval >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                                dval <= static_cast<double>((std::numeric_limits<float>::max)()));
+                    break;
+                }
+                default:
+                    // 'D' (double) already spans the full range of number_float_t
+                    break;
+            }
+            if (!in_range)
+            {
+                return true;
+            }
+        }
+
         oa->write_character('[');
         oa->write_character('$');
         oa->write_character(dtype);
diff --git a/tests/src/unit-bjdata.cpp b/tests/src/unit-bjdata.cpp
index 7d0dd5ff2..78ddf5d8c 100644
--- a/tests/src/unit-bjdata.cpp
+++ b/tests/src/unit-bjdata.cpp
@@ -2776,6 +2776,53 @@ TEST_CASE("BJData")
                 CHECK(out_num.at(0) == '{');
                 CHECK(json::from_bjdata(out_num) == j_num);
             }
+
+            SECTION("ndarray with out-of-range _ArrayData_ elements stays as object")
+            {
+                // each element is cast to the (possibly narrower) C++ type
+                // named by _ArrayType_ before being written; a value that
+                // does not fit that type would silently wrap instead of
+                // being reported, so such an object falls back to a plain
+                // object encoding that still round-trips (see GitHub issue #5403)
+
+                // an unsigned element that does not fit uint8
+                json const j_uint8 = json({{"_ArrayType_", "uint8"}, {"_ArraySize_", {2}}, {"_ArrayData_", {1, 256}}});
+                const auto out_uint8 = json::to_bjdata(j_uint8);
+                CHECK(out_uint8.at(0) == '{');
+                CHECK(json::from_bjdata(out_uint8) == j_uint8);
+
+                // a signed element that does not fit int8
+                json const j_int8 = json({{"_ArrayType_", "int8"}, {"_ArraySize_", {2}}, {"_ArrayData_", {1, 200}}});
+                const auto out_int8 = json::to_bjdata(j_int8);
+                CHECK(out_int8.at(0) == '{');
+                CHECK(json::from_bjdata(out_int8) == j_int8);
+
+                // a negative element is likewise out of range for an
+                // unsigned _ArrayType_
+                json const j_uint16_neg = json({{"_ArrayType_", "uint16"}, {"_ArraySize_", {2}}, {"_ArrayData_", {1, -1}}});
+                const auto out_uint16_neg = json::to_bjdata(j_uint16_neg);
+                CHECK(out_uint16_neg.at(0) == '{');
+                CHECK(json::from_bjdata(out_uint16_neg) == j_uint16_neg);
+
+                // a double element that overflows to infinity when narrowed
+                // to the "single" (float) precision named by _ArrayType_
+                json const j_single = json({{"_ArrayType_", "single"}, {"_ArraySize_", {2}}, {"_ArrayData_", {1.5, 1e40}}});
+                const auto out_single = json::to_bjdata(j_single);
+                CHECK(out_single.at(0) == '{');
+                CHECK(json::from_bjdata(out_single) == j_single);
+
+                // in-range boundary values still use the compact ndarray encoding
+                json const j_uint8_ok = json({{"_ArrayType_", "uint8"}, {"_ArraySize_", {2}}, {"_ArrayData_", {0, 255}}});
+                CHECK(json::to_bjdata(j_uint8_ok) == std::vector<uint8_t>({'[', '$', 'U', '#', '[', 'i', 2, ']', 0, 255}));
+
+                json const j_int8_ok = json({{"_ArrayType_", "int8"}, {"_ArraySize_", {2}}, {"_ArrayData_", {-128, 127}}});
+                CHECK(json::to_bjdata(j_int8_ok) == std::vector<uint8_t>({'[', '$', 'i', '#', '[', 'i', 2, ']', 0x80, 0x7F}));
+
+                json const j_single_ok = json({{"_ArrayType_", "single"}, {"_ArraySize_", {1}}, {"_ArrayData_", {1.5}}});
+                const auto out_single_ok = json::to_bjdata(j_single_ok);
+                CHECK(out_single_ok.at(0) == '[');
+                CHECK(json::from_bjdata(out_single_ok) == json({1.5f}));
+            }
         }
     }