Datasette is a Python module which provides a web interface and a JSON API for SQLite files. But, in conjuntion with Datasette-Connectors, it 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-connectors to install both Datasette and Datasette-Connectors. Easy as pie!
You can use Datasette from the console in the traditional way:
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/
Or you can use Datasette in your own Python programs:
from datasette_connectors import monkey; monkey.patch_datasette()
from datasette_connectors.connectors import ConnectorList; ConnectorList.load()
For that, you need to patch the original Datasette and load the external connectors.
Read the Datasette documentation for more advanced options.