Datasette-PyTables provides a web interface and a JSON API for PyTables files, allowing them to be accessible for e.g. Javascript programs. It works in conjunction with Datasette-Core, a trivial fork of the original Datasette, which provides a web interface for SQLite files. This fork is able to work with SQLite files, like the original project, but can accept external connectors for any kind of database files, so you can develop your own connector for your favourite data container if you want (read developers doc).
Run pip install datasette-pytables
to install both the forked version of Datasette and the PyTables connector. Easy as pie!
datasette serve path/to/data.h5
This will start a web server on port 8001; then you can access to your data visiting http://localhost:8001/
Read the Datasette documentation for more advanced options.