The shared hosting can be used as a mysql host as moneybrz said above. First 1000MB is free at midnight as above, for more space it's $5 per 1000MB up to a max of 5000MB for larger accounts (one time fee).
That said, if you need space beyond 5000MB or you want control over mysql's configuration/version/etc., you can buy a VPS for as little as $4/month, though if you plan on running large queries on the database server an extra GB of RAM to improve performance would be a good idea: https://heliohost.org/vps/ (there's a wait list at the moment).