diff --git a/requires/installation.txt b/requires/installation.txt
index 07af68f..e0dcd27 100644
--- a/requires/installation.txt
+++ b/requires/installation.txt
@@ -1 +1 @@
-tornado>=3.1,<5
+tornado>=3.1,<6
diff --git a/sprockets/http/app.py b/sprockets/http/app.py
index 09bb19d..54794ec 100644
--- a/sprockets/http/app.py
+++ b/sprockets/http/app.py
@@ -2,6 +2,11 @@ import logging
 import sys
 
 from tornado import concurrent, web
+import tornado
+
+ASYNCIO_TORNADO = tornado.version_info[0] >= 5
+if ASYNCIO_TORNADO:
+    import asyncio
 
 
 class _ShutdownHandler(object):
@@ -40,13 +45,18 @@ class _ShutdownHandler(object):
 
     def _maybe_stop(self):
         now = self.io_loop.time()
-        if (now < self.__deadline and
-                (self.io_loop._callbacks or self.io_loop._timeouts)):
+        if now < self.__deadline and self._ioloop_has_tasks():
             self.io_loop.add_timeout(now + 1, self._maybe_stop)
         else:
             self.io_loop.stop()
             self.logger.info('stopped IOLoop')
 
+    def _ioloop_has_tasks(self):
+        if ASYNCIO_TORNADO:
+            return bool(asyncio.Task.all_tasks())
+        else:
+            return bool(self.io_loop._callbacks or self.io_loop._timeouts)
+
 
 class CallbackManager(object):
     """
@@ -120,6 +130,10 @@ class CallbackManager(object):
         for callback in self.on_shutdown_callbacks:
             try:
                 maybe_future = callback(self.tornado_application)
+
+                if ASYNCIO_TORNADO and asyncio.iscoroutine(maybe_future):
+                        maybe_future = asyncio.create_task(maybe_future)
+
                 if concurrent.is_future(maybe_future):
                     shutdown.add_future(maybe_future)
                     running_async = True
diff --git a/tests.py b/tests.py
index b37e58c..0221508 100644
--- a/tests.py
+++ b/tests.py
@@ -448,6 +448,7 @@ class RunnerTests(MockHelper, unittest.TestCase):
             self.io_loop.add_callback_from_signal.assert_called_once_with(
                 runner._shutdown)
 
+    @unittest.skipUnless(tornado.version_info < (5,), '')
     def test_that_shutdown_waits_for_callbacks(self):
         def add_timeout(_, callback):
             self.io_loop._callbacks.pop()
@@ -461,6 +462,7 @@ class RunnerTests(MockHelper, unittest.TestCase):
         self.io_loop.stop.assert_called_once_with()
         self.assertEqual(self.io_loop.add_timeout.call_count, 2)
 
+    @unittest.skipUnless(tornado.version_info < (5,), '')
     def test_that_shutdown_waits_for_timeouts(self):
         def add_timeout(_, callback):
             self.io_loop._timeouts.pop()