diff --git a/babel/dates.py b/babel/dates.py
index 69610a7f0..c99e6401e 100644
--- a/babel/dates.py
+++ b/babel/dates.py
@@ -1330,7 +1330,12 @@ def parse_date(
     day = int(numbers[indexes['D']])
     if month > 12:
         month, day = day, month
-    return datetime.date(year, month, day)
+    try:
+        return datetime.date(year, month, day)
+    except ValueError as e:
+        raise ParseError(
+            f"'{string}' does not represent a valid date for format '{fmt.pattern}'"
+        ) from e
 
 
 def parse_time(
@@ -1395,7 +1400,12 @@ def parse_time(
         minute = int(numbers[indexes['M']])
         if len(numbers) > 2:
             second = int(numbers[indexes['S']])
-    return datetime.time(hour, minute, second)
+    try:
+        return datetime.time(hour, minute, second)
+    except ValueError as e:
+        raise ParseError(
+            f"'{string}' does not represent a valid time for format '{fmt.pattern}'"
+        ) from e
 
 
 class DateTimePattern:
diff --git a/tests/test_dates.py b/tests/test_dates.py
index 12bb23433..ecd4ec742 100644
--- a/tests/test_dates.py
+++ b/tests/test_dates.py
@@ -724,6 +724,20 @@ def test_parse_errors(case, func):
         func(case, locale='en_US')
 
 
+def test_parse_date_out_of_range():
+    with pytest.raises(dates.ParseError) as excinfo:
+        dates.parse_date('2005-02-30', format='yyyy-MM-dd')
+    assert 'does not represent a valid date' in str(excinfo.value)
+    assert isinstance(excinfo.value.__cause__, ValueError)
+
+
+def test_parse_time_out_of_range():
+    with pytest.raises(dates.ParseError) as excinfo:
+        dates.parse_time('25:00', format='HH:mm')
+    assert 'does not represent a valid time' in str(excinfo.value)
+    assert isinstance(excinfo.value.__cause__, ValueError)
+
+
 def test_datetime_format_get_week_number():
     format = dates.DateTimeFormat(date(2006, 1, 8), Locale.parse('de_DE'))
     assert format.get_week_number(6) == 1