diff --git a/kernel_gateway/tests/test_gatewayapp.py b/kernel_gateway/tests/test_gatewayapp.py
index aab009a..3216904 100644
--- a/kernel_gateway/tests/test_gatewayapp.py
+++ b/kernel_gateway/tests/test_gatewayapp.py
@@ -7,7 +7,7 @@
 import os
 from kernel_gateway.gatewayapp import KernelGatewayApp, ioloop
 from ..notebook_http.swagger.handlers import SwaggerSpecHandler
-from tornado.testing import AsyncHTTPTestCase, LogTrapTestCase
+from tornado.testing import AsyncHTTPTestCase, ExpectLog
 
 RESOURCES = os.path.join(os.path.dirname(__file__), 'resources')
 
@@ -66,7 +66,7 @@ def test_config_env_vars(self):
         self.assertEqual(app.certfile, '/test/fake.crt')
         self.assertEqual(app.client_ca, '/test/fake_ca.crt')
 
-class TestGatewayAppBase(AsyncHTTPTestCase, LogTrapTestCase):
+class TestGatewayAppBase(AsyncHTTPTestCase, ExpectLog):
     """Base class for integration style tests using HTTP/Websockets against an
     instance of the gateway app.
 
diff --git a/kernel_gateway/tests/test_notebook_http.py b/kernel_gateway/tests/test_notebook_http.py
index 8bc915d..50e5eac 100644
--- a/kernel_gateway/tests/test_notebook_http.py
+++ b/kernel_gateway/tests/test_notebook_http.py
@@ -381,13 +381,25 @@ def test_concurrent_request_should_not_be_blocked(self):
             method='GET',
             raise_error=False
         )
-        self.assertTrue(response_long_running.running(), 'Long HTTP Request is not running')
+        if callable(getattr(response_long_running, 'done', "")):
+            # Tornado 5
+            self.assertFalse(response_long_running.done(), 'Long HTTP Request is not running')
+        else:
+            # Tornado 4
+            self.assertTrue(response_long_running.running(), 'Long HTTP Request is not running')
+
         response_short_running = yield self.http_client.fetch(
             self.get_url('/sleep/3'),
             method='GET',
             raise_error=False
         )
-        self.assertTrue(response_long_running.running(), 'Long HTTP Request is not running')
+        if callable(getattr(response_long_running, 'done', "")):
+            # Tornado 5
+            self.assertFalse(response_long_running.done(), 'Long HTTP Request is not running')
+        else:
+            # Tornado 4
+            self.assertTrue(response_long_running.running(), 'Long HTTP Request is not running')
+
         self.assertEqual(response_short_running.code, 200, 'Short HTTP Request did not return proper status code of 200')
 
     @gen_test
diff --git a/requirements.txt b/requirements.txt
index 9a36160..f20794a 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,5 +2,5 @@ jupyter_core>=4.0
 jupyter_client>=4.2.0
 notebook>=5.0.0
 traitlets>=4.2.0
-tornado>=4.2.0,<5.0
+tornado>=4.2.0
 requests>=2.7,<3.0
diff --git a/setup.py b/setup.py
index f009a1d..49e80f6 100644
--- a/setup.py
+++ b/setup.py
@@ -57,7 +57,7 @@
         'jupyter_client>=4.2.0',
         'notebook>=5.0.0,<6.0',
         'traitlets>=4.2.0',
-        'tornado>=4.2.0,<5.0',
+        'tornado>=4.2.0',
         'requests>=2.7,<3.0'
     ],
     classifiers=[