Updating MySQL version

I've got a Contao installation version 2.11. This is running with MySQL version 5.1.

We're now setting up a new version of the website on the same server – but separately from the current installation – using Contao 3.3.5

I thought it might be a good idea to now update MySQL to a later version. The hosting company say they could update to MySQL 5.3.

I want to check: Could this in any way affect the current Contao 2.11 site? Or can I just give them the go-ahead to update, and the Contao 2.11 site will just continuing to work as before?

Many thanks for your answers.