diff -r c81dd9fe0d87 Lib/test/test_bigmem.py
--- a/Lib/test/test_bigmem.py	Mon Apr 13 11:30:56 2015 -0400
+++ b/Lib/test/test_bigmem.py	Mon Apr 13 16:12:34 2015 -0400
@@ -11,6 +11,7 @@
 from test import support
 from test.support import bigmemtest, _1G, _2G, _4G
 
+from ctypes import c_voidp, sizeof
 import unittest
 import operator
 import sys
@@ -905,9 +906,8 @@
     def test_repeat_large_2(self, size):
         return self.basic_test_repeat(size)
 
-    @bigmemtest(size=_1G - 1, memuse=9)
-    def test_from_2G_generator(self, size):
-        self.skipTest("test needs much more memory than advertised, see issue5438")
+    @bigmemtest(size=_1G - 1, memuse=sys.getsizeof(_1G - 1) + sizeof(c_voidp))
+    def test_from_2G_iterable(self, size):
         try:
             t = tuple(range(size))
         except MemoryError:
@@ -919,6 +919,22 @@
                 count += 1
             self.assertEqual(count, size)
 
+    @bigmemtest(size=_1G - 1, memuse=sys.getsizeof(_1G - 1) + sizeof(c_voidp))
+    def test_from_2G_generator(self, size):
+        def no_len_range(a):
+            yield from range(a)
+
+        try:
+            t = tuple(no_len_range(size))
+        except MemoryError:
+            pass # acceptable on 32-bit
+        else:
+            count = 0
+            for item in t:
+                self.assertEqual(item, count)
+                count += 1
+            self.assertEqual(count, size)
+
     @bigmemtest(size=_1G - 25, memuse=9)
     def test_from_almost_2G_generator(self, size):
         self.skipTest("test needs much more memory than advertised, see issue5438")