diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
index 557e952..56e9083 100644
--- a/Lib/test/test_complex.py
+++ b/Lib/test/test_complex.py
@@ -467,6 +467,16 @@
         self.assertEqual(format(3+0j, ''), str(3+0j))
         self.assertEqual(format(3.2+0j, ''), str(3.2+0j))
 
+        # empty presentation type should still be analogous to str,
+        # even when format string is nonempty (issue #5920).
+        self.assertEqual(format(3.2+0j, '-'), str(3.2+0j))
+        self.assertEqual(format(3.2+0j, '<'), str(3.2+0j))
+        z = 4/7. - 100j/7.
+        self.assertEqual(format(z, ''), str(z))
+        self.assertEqual(format(z, '-'), str(z))
+        self.assertEqual(format(z, '<'), str(z))
+        self.assertEqual(format(z, '10'), str(z))
+
         self.assertEqual(format(1+3j, 'g'), '1+3j')
         self.assertEqual(format(3j, 'g'), '0+3j')
         self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j')
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index 971c14f..1c6c412 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -257,6 +257,53 @@
             self.assertEquals(math.atan2(float('-1e-1000'), -1),
                               math.atan2(-0.0, -1))
 
+    def test_format(self):
+        # these should be rewritten to use both format(x, spec) and
+        # x.__format__(spec)
+
+        self.assertEqual(format(0.0, 'f'), '0.000000')
+
+        # the default is 'g', except for empty format spec
+        self.assertEqual(format(0.0, ''), '0.0')
+        self.assertEqual(format(0.01, ''), '0.01')
+        self.assertEqual(format(0.01, 'g'), '0.01')
+
+        # empty presentation type should format in the same way as str
+        # (issue 5920)
+        x = 100/7.
+        self.assertEqual(format(x, ''), str(x))
+        self.assertEqual(format(x, '-'), str(x))
+        self.assertEqual(format(x, '>'), str(x))
+        self.assertEqual(format(x, '2'), str(x))
+
+        self.assertEqual(format(1.0, 'f'), '1.000000')
+
+        self.assertEqual(format(-1.0, 'f'), '-1.000000')
+
+        self.assertEqual(format( 1.0, ' f'), ' 1.000000')
+        self.assertEqual(format(-1.0, ' f'), '-1.000000')
+        self.assertEqual(format( 1.0, '+f'), '+1.000000')
+        self.assertEqual(format(-1.0, '+f'), '-1.000000')
+
+        # % formatting
+        self.assertEqual(format(-1.0, '%'), '-100.000000%')
+
+        # conversion to string should fail
+        self.assertRaises(ValueError, format, 3.0, "s")
+
+        # other format specifiers shouldn't work on floats,
+        #  in particular int specifiers
+        for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] +
+                            [chr(x) for x in range(ord('A'), ord('Z')+1)]):
+            if not format_spec in 'eEfFgGn%':
+                self.assertRaises(ValueError, format, 0.0, format_spec)
+                self.assertRaises(ValueError, format, 1.0, format_spec)
+                self.assertRaises(ValueError, format, -1.0, format_spec)
+                self.assertRaises(ValueError, format, 1e100, format_spec)
+                self.assertRaises(ValueError, format, -1e100, format_spec)
+                self.assertRaises(ValueError, format, 1e-100, format_spec)
+                self.assertRaises(ValueError, format, -1e-100, format_spec)
+
     @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
                          "test requires IEEE 754 doubles")
     def test_format_testfile(self):