diff --git a/python-distributed.spec b/python-distributed.spec
index 7e97fdd..2f158f2 100644
--- a/python-distributed.spec
+++ b/python-distributed.spec
@@ -47,7 +47,7 @@ Requires:       python-six
 Requires:       python-sortedcontainers
 Requires:       python-tblib
 Requires:       python-toolz >= 0.7.4
-Requires:       python-tornado >= 4.5.1
+Requires:       python-tornado >= 5
 Requires:       python-zict >= 0.1.3
 BuildArch:      noarch
 %if %{with test}
@@ -63,7 +63,7 @@ BuildRequires:  %{python_module six}
 BuildRequires:  %{python_module sortedcontainers}
 BuildRequires:  %{python_module tblib}
 BuildRequires:  %{python_module toolz >= 0.7.4}
-BuildRequires:  %{python_module tornado >= 4.5.1}
+BuildRequires:  %{python_module tornado >= 5}
 BuildRequires:  %{python_module zict >= 0.1.3}
 %endif
 %python_subpackages