Q: I just got a refurbished iMac i5 it came with mountain lion and I can't use that for my job I need snow leopard or lion os can I reinstall snow leopard with a disk my Mac was built in may of 2011

Probably not, because it is a system specific disc for that iMac model.

see > Don't install a version of Mac OS X earlier than what came with your Mac

You may want to check out Mactracker  mactracker.ca

You can download it form the app store as well.

I believe all but the newest imacs will run Snow Leopard (10.6).

Your query is somewhat ambiguous.

What disc are you trying to use?

If it's a retail SL disc, it won't boot or install on a 2011 iMac.

The retail disc is 10.6.3, Your iMac would have originally shipped with 10.6.6 or possibly 10.6.7.

You can attempt to get copies of the original discs by calling Apple Customer Services with the serial no. of the Mac and a credit card.

A workaround is to use another Mac to install 10.6.3 on an external HDD, and update that to 10.6.8 with the combo installer.

Connect to the new Mac and boot from the external by holding down the option (alt) key on start up and choosing the external from the manager.

Then use Disk Utility  from the external to erase the Mac's HDD. Select the physical drive - the top entry with the maker's name and size in order to erase the Recovery partition as well as Macintosh HD.

Then clone the SL installation to the Mac using the Restore function in DU.

Did we ever figure out if Apple applied some firmware update to those Macs after the release of Lion that prevented booting Snow, even from 10.6.8, even though that model may originally have shipped with Snow?

Not for certain, and I've not seen any more recent reports directly affecting the issue.

I've seen a couple of threads in the last month or so that may or may not be related, but I don't have time to follow them up, I'm afraid.

OK, ta.