I'm not a pro or anything but, am training for my first 110 mile. Been using a 10 speed 12-25 cassette and 34/50 compact double crank, I found going up hills very challenging. Now if I was to upgrade to a new cassette, what would the best gear ratio be for my needs?

You could try a 12-27 which should work with your current derailleur.

You might also want to look into a coach or getting someone to help you with hills. For example, one workout a week of hill repeats might help a lot. You could also try riding fairly easy for much of a ride but pressing hard on hills. After a while with either of these types of training, you'll probably climb better than you do now. It may still be tough but you may just feel more comfortable or confident.

You have to figure that out for yourself. It depends on your fitness, your pedaling style on climbs (do you need to spin or are you ok at low rpms), and the climbs you're doing. If 34x25 isn't enough then you need lower gearing. Since you're doing an extra long ride and presumeably it has climbs, I'd suggest a 12-30. Going from 25t to 27t isn't that much lower. Shimano makes 12-30 cassettes. I have been able to use a 30t cog with Sram Red 2012, and with a 7900 derailleur on a Shimano bike. It may not work with older Shimano, but you can put a 7900 or the Ultegra equivalent derailleur on an older system. That's what I did.

If your 110 mile ride has climbs, then you need to do climbs in training to prepare. When training for a race or ride with lots of climbing I like to do repeats on the local long (hour to hour and a half) climbs, and shorter climbs during the week. Pretty much any climbing you do will improve your climbing but try to make it event specific. Doing two minute hill intervals won't train you well for a race with multiple two hour climbs.

http://www.ebay.com/itm/2012-Shimano-Ul ... 7fc&_uhb=1 great deal too but, it doesn't say anywhere if it will be compatible with my 5700 105 RD

It will probably work. 5700 has the same geometry as 7900. But it depends on your frame's hanger length. You may need to adjust the B screw, and you may need a longer chain. If you're not comfortable doing that, take it to the LBS.