diff --git a/docs/mkdocs/docs/api/operator_gtgt.md b/docs/mkdocs/docs/api/operator_gtgt.md
index e1d24d47f..a9ba17564 100644
--- a/docs/mkdocs/docs/api/operator_gtgt.md
+++ b/docs/mkdocs/docs/api/operator_gtgt.md
@@ -33,17 +33,44 @@ A UTF-8 byte order mark is silently ignored.
 Invalid Unicode escapes and unpaired surrogates in the input are reported as
 [`parse_error.101`](../home/exceptions.md#jsonexceptionparse_error101) with a detailed message.
 
-`operator>>` parses exactly one JSON value and leaves the stream positioned right after it, so it can be called
-repeatedly to read a sequence of concatenated JSON values from the same stream:
+`operator>>` parses exactly one JSON value, so it can be called repeatedly to read a sequence of concatenated JSON
+values from the same stream:
 
 ```cpp
 json j1, j2;
-input >> j1;  // parses the first value, stream now positioned right after it
+input >> j1;  // parses the first value
 input >> j2;  // parses the next value
 ```
 
-Note this does **not** work for [JSON Lines](../features/parsing/json_lines.md) (newline-delimited JSON) input --
-see that page for why and for the recommended alternative.
+!!! warning "A number must be followed by whitespace"
+
+    A number is only terminated by the character that follows it. That character is read from the stream to detect the
+    end of the number, and it is **not** put back. When a value that is a number is immediately followed by the next
+    value, the first character of that next value is lost:
+
+    ```cpp
+    std::istringstream input("1true");
+    json j1, j2;
+    input >> j1;  // j1 == 1
+    input >> j2;  // throws parse_error.101: the stream now starts at "rue"
+    ```
+
+    Separating the values with whitespace avoids this, because the character that is eaten is then the separator:
+
+    ```cpp
+    std::istringstream input("1 true");
+    json j1, j2;
+    input >> j1;  // j1 == 1
+    input >> j2;  // j2 == true
+    ```
+
+    Only numbers are affected. Values ending in a self-delimiting character do not read past themselves, so
+    `truefalse`, `[1][2]`, `{"a":1}{"b":2}`, and `"a""b"` can be read back to back without a separator.
+
+    This is tracked in [#5340](https://github.com/nlohmann/json/issues/5340).
+
+Note that reading concatenated values does **not** work for [JSON Lines](../features/parsing/json_lines.md)
+(newline-delimited JSON) input -- see that page for why and for the recommended alternative.
 
 !!! warning "Deprecation"
 
diff --git a/docs/mkdocs/docs/features/parsing/json_lines.md b/docs/mkdocs/docs/features/parsing/json_lines.md
index cda6f37c7..fb1481819 100644
--- a/docs/mkdocs/docs/features/parsing/json_lines.md
+++ b/docs/mkdocs/docs/features/parsing/json_lines.md
@@ -49,4 +49,5 @@ JSON Lines input with more than one value is treated as invalid JSON by the [`pa
     with a JSON Lines input does not work, because the parser will try to parse one value after the last one.
 
     This is different from parsing a stream of *concatenated* (non-newline-delimited) JSON values, for which
-    `operator>>` does work -- see its [notes](../../api/operator_gtgt.md#notes) for details.
+    `operator>>` does work, provided that a value that is a number is followed by whitespace -- see its
+    [notes](../../api/operator_gtgt.md#notes) for details.