diff --git a/src/backend/executor/functions.c b/src/backend/executor/functions.c
index 84398e8a960..f974febeee5 100644
--- a/src/backend/executor/functions.c
+++ b/src/backend/executor/functions.c
@@ -949,6 +949,11 @@ check_sql_fn_retval(Oid func_id, Oid rettype, List *queryTreeList,
 		 * This can happen, for example, where the body of the function is
 		 * 'SELECT func2()', where func2 has the same return type as the
 		 * function that's calling it.
+		 *
+		 * XXX Note that if rettype is RECORD, the IsBinaryCoercible check
+		 * will succeed for any composite restype.  For the moment we rely on
+		 * runtime type checking to catch any discrepancy, but it'd be nice to
+		 * do better at parse time.
 		 */
 		if (tlistlen == 1)
 		{
diff --git a/src/backend/optimizer/util/clauses.c b/src/backend/optimizer/util/clauses.c
index 7029ee1738d..bc5df1f6f97 100644
--- a/src/backend/optimizer/util/clauses.c
+++ b/src/backend/optimizer/util/clauses.c
@@ -2289,6 +2289,10 @@ evaluate_function(Oid funcid, Oid result_type, List *args,
  * We must also beware of changing the volatility or strictness status of
  * functions by inlining them.
  *
+ * Also, at the moment we can't inline functions returning RECORD.  This
+ * doesn't work in the general case because it discards information such
+ * as OUT-parameter declarations.
+ *
  * Returns a simplified expression if successful, or NULL if cannot
  * simplify the function.
  */
@@ -2320,6 +2324,7 @@ inline_function(Oid funcid, Oid result_type, List *args,
 	if (funcform->prolang != SQLlanguageId ||
 		funcform->prosecdef ||
 		funcform->proretset ||
+		funcform->prorettype == RECORDOID ||
 		funcform->pronargs != list_length(args))
 		return NULL;
 
diff --git a/src/test/regress/expected/rangefuncs.out b/src/test/regress/expected/rangefuncs.out
index 49fc121f04f..a043bc1d338 100644
--- a/src/test/regress/expected/rangefuncs.out
+++ b/src/test/regress/expected/rangefuncs.out
@@ -528,3 +528,23 @@ CREATE FUNCTION bad (f1 int, out f2 anyelement, out f3 anyarray)
 AS 'select $1, array[$1,$1]' LANGUAGE sql;
 ERROR:  cannot determine result data type
 DETAIL:  A function returning "anyarray" or "anyelement" must have at least one argument of either type.
+-- check handling of a SQL function with multiple OUT params (bug #5777)
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2.1) $$ language sql;
+select * from foobar();
+ column1 | column2 
+---------+---------
+       1 |     2.1
+(1 row)
+
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2) $$ language sql;
+select * from foobar();  -- fail
+ERROR:  function return row and query-specified return row do not match
+DETAIL:  Returned type integer at ordinal position 2, but query expects numeric.
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2.1, 3) $$ language sql;
+select * from foobar();  -- fail
+ERROR:  function return row and query-specified return row do not match
+DETAIL:  Returned row contains 3 attributes, but query expects 2.
+drop function foobar();
diff --git a/src/test/regress/sql/rangefuncs.sql b/src/test/regress/sql/rangefuncs.sql
index 50495897acd..06bbd1b537d 100644
--- a/src/test/regress/sql/rangefuncs.sql
+++ b/src/test/regress/sql/rangefuncs.sql
@@ -261,3 +261,22 @@ DROP FUNCTION dup(anyelement);
 -- fails, no way to deduce outputs
 CREATE FUNCTION bad (f1 int, out f2 anyelement, out f3 anyarray)
 AS 'select $1, array[$1,$1]' LANGUAGE sql;
+
+-- check handling of a SQL function with multiple OUT params (bug #5777)
+
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2.1) $$ language sql;
+
+select * from foobar();
+
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2) $$ language sql;
+
+select * from foobar();  -- fail
+
+create or replace function foobar(out integer, out numeric) as
+$$ select (1, 2.1, 3) $$ language sql;
+
+select * from foobar();  -- fail
+
+drop function foobar();