diff --git a/include/nlohmann/detail/json_pointer.hpp b/include/nlohmann/detail/json_pointer.hpp
index 576ba62cc..247c5babb 100644
--- a/include/nlohmann/detail/json_pointer.hpp
+++ b/include/nlohmann/detail/json_pointer.hpp
@@ -748,6 +748,20 @@ class json_pointer
                         }
                     }
 
+                    // the reference token consists only of digits at this point (cf. checks
+                    // above); however, its numeric value might not be representable, in which
+                    // case array_index() would throw out_of_range.404/410 -- contains() must
+                    // not throw (see #5395), so such a reference token is treated as "not found"
+                    errno = 0; // strtoull() does not reset errno on success
+                    char* p_end = nullptr; // NOLINT(misc-const-correctness)
+                    const unsigned long long magnitude = std::strtoull(reference_token.c_str(), &p_end, 10); // NOLINT(runtime/int)
+                    if (JSON_HEDLEY_UNLIKELY(errno == ERANGE // the value exceeds ULLONG_MAX
+                                             || magnitude >= static_cast<unsigned long long>((std::numeric_limits<typename BasicJsonType::size_type>::max)()))) // NOLINT(runtime/int)
+                    {
+                        // the array index cannot be represented as size_type
+                        return false;
+                    }
+
                     const auto idx = array_index<BasicJsonType>(reference_token);
                     if (idx >= ptr->size())
                     {
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 31bfb869d..a8fff3e41 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -16394,6 +16394,20 @@ class json_pointer
                         }
                     }
 
+                    // the reference token consists only of digits at this point (cf. checks
+                    // above); however, its numeric value might not be representable, in which
+                    // case array_index() would throw out_of_range.404/410 -- contains() must
+                    // not throw (see #5395), so such a reference token is treated as "not found"
+                    errno = 0; // strtoull() does not reset errno on success
+                    char* p_end = nullptr; // NOLINT(misc-const-correctness)
+                    const unsigned long long magnitude = std::strtoull(reference_token.c_str(), &p_end, 10); // NOLINT(runtime/int)
+                    if (JSON_HEDLEY_UNLIKELY(errno == ERANGE // the value exceeds ULLONG_MAX
+                                             || magnitude >= static_cast<unsigned long long>((std::numeric_limits<typename BasicJsonType::size_type>::max)()))) // NOLINT(runtime/int)
+                    {
+                        // the array index cannot be represented as size_type
+                        return false;
+                    }
+
                     const auto idx = array_index<BasicJsonType>(reference_token);
                     if (idx >= ptr->size())
                     {
diff --git a/tests/src/unit-json_pointer.cpp b/tests/src/unit-json_pointer.cpp
index a8ed4a89e..4082de45c 100644
--- a/tests/src/unit-json_pointer.cpp
+++ b/tests/src/unit-json_pointer.cpp
@@ -319,6 +319,44 @@ TEST_CASE("JSON pointers")
 
                 CHECK_THROWS_WITH_AS(j[jp] = 1, throw_msg.c_str(), json::out_of_range&);
                 CHECK_THROWS_WITH_AS(j_const[jp] == 1, throw_msg.c_str(), json::out_of_range&);
+
+                // #5395: contains() must not throw for a reference token that is a
+                // syntactically valid array index but numerically exceeds ULLONG_MAX
+                // (causing strtoull() to set errno to ERANGE) -- it should just report
+                // that the pointer does not resolve to an element
+                CHECK(!j.contains(jp));
+                CHECK(!j_const.contains(jp));
+            }
+
+            {
+                // #5395: same as above, but using the exact reproduction from the issue
+                json::json_pointer const jp("/99999999999999999999");
+                std::string const throw_msg = "[json.exception.out_of_range.404] unresolved reference token '99999999999999999999'";
+
+                CHECK_THROWS_WITH_AS(j[jp] = 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j_const[jp] == 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j.at(jp) = 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j_const.at(jp) == 1, throw_msg.c_str(), json::out_of_range&);
+
+                CHECK(!j.contains(jp));
+                CHECK(!j_const.contains(jp));
+            }
+
+            {
+                // #5395: a reference token that is numerically representable in
+                // unsigned long long but exceeds size_type's max (e.g. ULLONG_MAX
+                // itself on typical 64-bit platforms, where size_type's max equals
+                // ULLONG_MAX) must not make contains() throw either
+                json::json_pointer const jp("/18446744073709551615");
+                std::string const throw_msg = "[json.exception.out_of_range.410] array index 18446744073709551615 exceeds size_type";
+
+                CHECK_THROWS_WITH_AS(j[jp] = 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j_const[jp] == 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j.at(jp) = 1, throw_msg.c_str(), json::out_of_range&);
+                CHECK_THROWS_WITH_AS(j_const.at(jp) == 1, throw_msg.c_str(), json::out_of_range&);
+
+                CHECK(!j.contains(jp));
+                CHECK(!j_const.contains(jp));
             }
 
             // on some machines, the check below is not constant
@@ -334,6 +372,10 @@ TEST_CASE("JSON pointers")
 
                 CHECK_THROWS_WITH_AS(j[jp] = 1, throw_msg.c_str(), json::out_of_range&);
                 CHECK_THROWS_WITH_AS(j_const[jp] == 1, throw_msg.c_str(), json::out_of_range&);
+
+                // #5395: contains() must not throw for a reference token exceeding size_type's max
+                CHECK(!j.contains(jp));
+                CHECK(!j_const.contains(jp));
             }
 
             DOCTEST_MSVC_SUPPRESS_WARNING_POP