You'd normally do this by setting up multiple tables within the same database. So you might have a database called admin with tables called customers, employees and products. This is an absolutely standard thing to do and MySQL should have no problems at all.
If you really need data from seperate databases then this is also possible, but, like you say, you will need to open seperate connections to each one, which may be a little slow for large sites and/or large sets of data.
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