diff --git a/.travis.yml b/.travis.yml
index 904fb9966..fd4162146 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -24,11 +24,11 @@ matrix:
     services: docker
     env: PYTHON=3.6 CPP=17 GCC=7
   - os: linux
-    env: PYTHON=3.6 CPP=17 CLANG=4.0
+    env: PYTHON=3.6 CPP=17 CLANG=5.0
     addons:
       apt:
-        sources: [deadsnakes, llvm-toolchain-trusty-4.0]
-        packages: [python3.6-dev python3.6-venv clang-4.0 llvm-4.0-dev, lld-4.0]
+        sources: [deadsnakes, llvm-toolchain-trusty-5.0, ubuntu-toolchain-r-test]
+        packages: [python3.6-dev python3.6-venv clang-5.0 llvm-5.0-dev, lld-5.0]
   - os: osx
     osx_image: xcode7.3
     env: PYTHON=2.7 CPP=14 CLANG
@@ -153,13 +153,13 @@ install:
         libeigen3-dev libboost-dev cmake make ${COMPILER_PACKAGES} && break; done"
   else
 
-    if [ "$CLANG" = "4.0" ]; then
+    if [ "$CLANG" = "5.0" ]; then
       if ! [ -d ~/.local/include/c++/v1 ]; then
-        # Neither debian nor llvm provide a libc++ 4.0 deb; luckily it's fairly quick
+        # Neither debian nor llvm provide a libc++ 5.0 deb; luckily it's fairly quick
         # to build, install (and cache), so do it ourselves:
         git clone --depth=1 https://github.com/llvm-mirror/llvm.git llvm-source
-        git clone https://github.com/llvm-mirror/libcxx.git llvm-source/projects/libcxx -b release_40
-        git clone https://github.com/llvm-mirror/libcxxabi.git llvm-source/projects/libcxxabi -b release_40
+        git clone https://github.com/llvm-mirror/libcxx.git llvm-source/projects/libcxx -b release_50
+        git clone https://github.com/llvm-mirror/libcxxabi.git llvm-source/projects/libcxxabi -b release_50
         mkdir llvm-build && cd llvm-build
         # Building llvm requires a newer cmake than is provided by the trusty container:
         CMAKE=cmake-3.8.0-Linux-x86_64