diff --git a/python/paddle/fluid/tests/unittests/autograd/test_primapi.py b/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
index dc52c5bc33b480401b7689ab4a2f7a89510e50b5..ec06eda66f8e56f5b79281d347d51568c9d01ec4 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
@@ -161,7 +161,7 @@ class TestGrad(unittest.TestCase):
         exe = paddle.static.Executor(place)
         exe.run(startup)
         outs = exe.run(main, feed=feed, fetch_list=fetch_list)
-        np.allclose(outs, result)
+        np.testing.assert_allclose(outs, result, rtol=1e-5, atol=1e-5)
         paddle.incubate.autograd.disable_prim()
 
     def test_fourth_order(self):
@@ -196,7 +196,43 @@ class TestGrad(unittest.TestCase):
         exe = paddle.static.Executor(place)
         exe.run(startup)
         outs = exe.run(main, feed=feed, fetch_list=fetch_list)
-        np.allclose(outs, result)
+        np.testing.assert_allclose(outs, result, rtol=1e-5, atol=1e-5)
+        paddle.incubate.autograd.disable_prim()
+
+    def test_fifth_order(self):
+        paddle.incubate.autograd.enable_prim()
+        main = paddle.static.Program()
+        startup = paddle.static.Program()
+        with paddle.static.program_guard(main, startup):
+            x = paddle.static.data(name='x', shape=[1], dtype='float32')
+            x2 = paddle.multiply(x, x)
+            x3 = paddle.multiply(x2, x)
+            x4 = paddle.multiply(x3, x)
+            x5 = paddle.multiply(x4, x)
+            x6 = paddle.multiply(x5, x)
+            out = x6 + x5
+
+            grad1, = paddle.incubate.autograd.grad([out], [x])
+            grad2, = paddle.incubate.autograd.grad([grad1], [x])
+            grad3, = paddle.incubate.autograd.grad([grad2], [x])
+            grad4, = paddle.incubate.autograd.grad([grad3], [x])
+            grad5, = paddle.incubate.autograd.grad([grad4], [x])
+
+            paddle.incubate.autograd.prim2orig()
+
+        feed = {
+            x.name: np.array([2.]).astype('float32'),
+        }
+        fetch_list = [grad5.name]
+        result = [np.array([1560.0])]
+
+        place = paddle.CPUPlace()
+        if paddle.device.is_compiled_with_cuda():
+            place = paddle.CUDAPlace(0)
+        exe = paddle.static.Executor(place)
+        exe.run(startup)
+        outs = exe.run(main, feed=feed, fetch_list=fetch_list)
+        np.testing.assert_allclose(outs, result, rtol=1e-5, atol=1e-5)
         paddle.incubate.autograd.disable_prim()
 
     def test_disable_prim(self):