The stock rear shock on an 05 FSR XC is...
a 6.5 eye to eye by 1.5 inch stoke. This is how shocks are measured. It means from one mounting eye to the other is 6.5 inches, and the shock compresses from full extension to bottom out 1.5 inches. It is not adviseable to put a longer shock on the bike. The suspension linkage and such were designed around that particular shock size. Adding a longer stroke shock can lead to clearance issues with the frame and suspension components. That being said, it can be done. But results are hard to predict. The next larger shock to your stock set up is a 7.5x1.75. This will add a total of 1 inch to your shock length, change the geometry of the bike a bit, and you'll only be getting around an 18mm travel increase. If you were to go with a 2 inch stroke shock you could get an additional 30mm of travel out of it. But like I said before, it isn't recommended by Specialized for sure. It is an expensive experiment that may or may not work out! And it may not be good for your bike either. Anyway, if you want more travel out of the bike give it a try. But once you have the new shock installed you need to make sure that you have NO CLEARANCE ISSUES when the suspension is a full extension or full compression. If ANY part touches any other at ANY time the mod is a NO GO!!! Contact between parts that aren't supposed to touch each other is BAD!
Anyway the bottom line is, the FSR XC was designed to have a 6.5 x 1.5 shock on it, which renders about 4" of travel. It performs best in this configuration. By increasing your shock length and stroke you may well compromise that peformance. And it may not be doable at all should you have clearance issues. And you could end up voiding one of the best frame warranties in the business. You can try it if you want. But for my money if you want a longer travel bike, get one. Leave the FSR as it is. It's a fine bike for it's intended purpose, XC/Trail. There is no real reason to increase the travel of the bike and risk any problems. Use it as intended and have fun with it. The increase in travel isn't worth the possible headaches.
Good Dirt