Add check for ES5 in CI

Author: GuillaumeGomez

Diff for: src/ci/docker/host-x86_64/mingw-check/Dockerfile

@@ -17,6 +17,11 @@ RUN apt-get update && apt-get install -y --no-install-recommends \
   pkg-config \
   mingw-w64
 
+RUN curl -sL https://nodejs.org/dist/v14.4.0/node-v14.4.0-linux-x64.tar.xz | tar -xJ
+ENV PATH="/node-v14.4.0-linux-x64/bin:${PATH}"
+# Install es-check
+RUN npm install es-check -g
+
 COPY scripts/sccache.sh /scripts/
 RUN sh /scripts/sccache.sh
 
@@ -29,4 +34,6 @@ ENV SCRIPT python3 ../x.py --stage 2 test src/tools/expand-yaml-anchors && \
            python3 ../x.py test --stage 0 src/tools/compiletest && \
            python3 ../x.py test --stage 2 src/tools/tidy && \
            python3 ../x.py doc --stage 0 library/std && \
-           /scripts/validate-toolstate.sh
+           /scripts/validate-toolstate.sh && \
+           # Runs checks to ensure that there are no ES5 issues in our JS code.
+           es-check es5 ../src/librustdoc/html/static/*.js