TC Upgrade *And* MySql Upgrade

Hi,

I have TC 5.1.5 and will be upgrading to TC 6.5.3.  The TC 5.1.5 uses mysql 5.0.77r3.el5.  I plan to use mysql 5.1.52r1.el6_0.1.

Can my current database backups (created via the "Administrator" menu) be used to create my db on TC6.5.3? Or, do I have to upgrade mysql while still on TC5.1.5 and then upgrade TC afterwards?

Put another way, can I simply import the TC 5.1.5 backup data into TC6.5.3 even if TC uses a newer mysql?

TIA,
-T