diff --git a/babel/src/test/resources/sql/big-query.iq b/babel/src/test/resources/sql/big-query.iq
index 0dce3ba5fdc..834bd65dd8d 100755
--- a/babel/src/test/resources/sql/big-query.iq
+++ b/babel/src/test/resources/sql/big-query.iq
@@ -2720,6 +2720,18 @@ SELECT TIMESTAMP(DATE "2008-12-25") AS timestamp_date;
 
 !ok
 
+# This tests the no-op TIMESTAMP and DATETIME functions.
+select TIMESTAMP(TIMESTAMP "2008-01-01 01:03:05") as ts,
+       DATETIME(DATETIME "2008-01-01 01:03:05") as dt;
++---------------------+---------------------+
+| ts                  | dt                  |
++---------------------+---------------------+
+| 2008-01-01 01:03:05 | 2008-01-01 01:03:05 |
++---------------------+---------------------+
+(1 row)
+
+!ok
+
 # All these timestamps should be equal.
 # This tests the BQ timestamp literal string formatter
 # (optional 'T', optional leading zeros, optional offset with conversion).
diff --git a/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java b/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
index 4dd9a390fa0..680301cc472 100644
--- a/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
+++ b/core/src/main/java/org/apache/calcite/sql/fun/SqlLibraryOperators.java
@@ -783,7 +783,9 @@ static RelDataType deriveTypeSplit(SqlOperatorBinding operatorBinding,
               // DATETIME(timestampLtz, timeZone)
               OperandTypes.sequence(
                   "DATETIME(TIMESTAMP WITH LOCAL TIME ZONE, VARCHAR)",
-                  OperandTypes.TIMESTAMP_LTZ, OperandTypes.CHARACTER)),
+                  OperandTypes.TIMESTAMP_LTZ, OperandTypes.CHARACTER),
+              // DATETIME(timestamp) -- This is a no-op.
+              OperandTypes.TIMESTAMP_NTZ),
           SqlFunctionCategory.TIMEDATE);
 
   /** The "TIME" function. It has the following overloads:
@@ -838,7 +840,9 @@ static RelDataType deriveTypeSplit(SqlOperatorBinding operatorBinding,
               OperandTypes.TIMESTAMP_NTZ,
               // TIMESTAMP(timestamp, timeZone)
               OperandTypes.sequence("TIMESTAMP(TIMESTAMP, VARCHAR)",
-                  OperandTypes.TIMESTAMP_NTZ, OperandTypes.CHARACTER)),
+                  OperandTypes.TIMESTAMP_NTZ, OperandTypes.CHARACTER),
+              // TIMESTAMP(timestampLtz) -- This is a no-op.
+              OperandTypes.TIMESTAMP_LTZ),
           SqlFunctionCategory.TIMEDATE);
 
   /** The "CURRENT_DATETIME([timezone])" function. */
diff --git a/core/src/test/java/org/apache/calcite/test/SqlToRelConverterTest.java b/core/src/test/java/org/apache/calcite/test/SqlToRelConverterTest.java
index 6a43a487f70..9eacf4f5ec2 100644
--- a/core/src/test/java/org/apache/calcite/test/SqlToRelConverterTest.java
+++ b/core/src/test/java/org/apache/calcite/test/SqlToRelConverterTest.java
@@ -5099,4 +5099,24 @@ void checkUserDefinedOrderByOver(NullCollation nullCollation) {
     String sql = "SELECT CAST(CAST(? AS INTEGER) AS CHAR)";
     sql(sql).ok();
   }
+
+  /**
+   * Test case for
+   * <a href="https://issues.apache.org/jira/browse/CALCITE-5508">DATETIME and TIMESTAMP constructor
+   * functions</a> that take single arguments with the same type as the function's return type.
+   *
+   * <p>The function counts as a no-op in this case.
+   */
+  @Test void testNoOpTimeDateFunctions() {
+    String sql = "SELECT TIMESTAMP(TIMESTAMP WITH LOCAL TIME ZONE '2023-12-21 12:34:56'), "
+        + "DATETIME(TIMESTAMP '2023-12-21 12:34:56') "
+        + "FROM emp";
+
+    fixture()
+        .withFactory(c ->
+            c.withOperatorTable(t ->
+                SqlValidatorTest.operatorTableFor(SqlLibrary.BIG_QUERY)))
+        .withSql(sql)
+        .ok();
+  }
 }
diff --git a/core/src/test/resources/org/apache/calcite/test/SqlToRelConverterTest.xml b/core/src/test/resources/org/apache/calcite/test/SqlToRelConverterTest.xml
index bf246b3a0b2..adad333e559 100644
--- a/core/src/test/resources/org/apache/calcite/test/SqlToRelConverterTest.xml
+++ b/core/src/test/resources/org/apache/calcite/test/SqlToRelConverterTest.xml
@@ -4927,6 +4927,17 @@ LogicalProject(SKILL=[ROW($0)])
   LogicalFilter(condition=[=($0, '')])
     LogicalProject(TYPE=[$0.TYPE])
       LogicalTableScan(table=[[CATALOG, SALES, DEPT_SINGLE]])
+]]>
+    </Resource>
+  </TestCase>
+  <TestCase name="testNoOpTimeDateFunctions">
+    <Resource name="sql">
+      <![CDATA[SELECT TIMESTAMP(TIMESTAMP WITH LOCAL TIME ZONE '2023-12-21 12:34:56'), DATETIME(TIMESTAMP '2023-12-21 12:34:56') FROM emp]]>
+    </Resource>
+    <Resource name="plan">
+      <![CDATA[
+LogicalProject(EXPR$0=[TIMESTAMP(2023-12-21 12:34:56:TIMESTAMP_WITH_LOCAL_TIME_ZONE(0))], EXPR$1=[DATETIME(2023-12-21 12:34:56)])
+  LogicalTableScan(table=[[CATALOG, SALES, EMP]])
 ]]>
     </Resource>
   </TestCase>