I think REACH is at least as inportant if not moreso than frime height. Also, you need to consider headtube height.

Are you riding mostly pavment and or groomed trails? Off-road riding means a lower toptube so you don't crush the family jewels during an unexpected stop/dismount.

I toured fire/logging/mountain roads 2-weeks at a time and did a lot of that on a 21" mtb frame and was 5'9".

A por image due to being scanned from a 3"x5" photo.

#01 Ready to Ride by Miele Man, on Flickr

For off road trail riding i like more clearance between the toptube and groin.

Here's are some of my other MTBs although they're all converted to drop bas.

IMG_3433 by Miele Man, on Flickr

IMG_0561 by Miele Man, on Flickr

IMG_3366 by Miele Man, on Flickr

IMG_3332 by Miele Man, on Flickr

None of these has 25cm (nearly 10 inches) of seatpost showing.

I'd say a 18" to 20" frame size should fit you. However that does depend on your leg and torso lengths.

Cheers