I guess I have to ask if you are wanting this for a road bike or tri/tt?
I have used a size medium in both situations (road and time trial) and I honestly think it depends on your torso length versus inseam. To help compare, I am 6' and with a 31" inseam and I ride a size large with a 13 cm stem and an FSA K-Force lite seat post with 2.5 cm set back with the saddle about mid-way back due to my road racing background in which I was reared in the laid out/euro (semi slam) riding position. In the past I have road raced on a size medium with a 14cm stem, an FSA K-Force Lite seat post (4 cm setback) and felt kind of cramped but again, I have a slightly longer torso in relation to inseam and my seat height is about ~73-74 cm from center of bottom bracket to top of saddle. Additionally, according to Giant's sizing chart, you are on the boundry as 5'11" can ride eithe r a size medium or a size large (http://www.giantbicycle.com/...0/050.600.100.asp#20). Keep in mind that a medium has a 55.5 cm effective top tube length whereas the large has a long 58.5 cm top tube length and in my case, I can ride a #1 or #2 Giant brand bladed seatpost with a size large frame or a #3 or #4 with a size medium frame and before I switched to the FSA seatpost, I used a #1 on the large frame and a #3 on the medium frame but to be honest, I felt a little cramped with the medium for road riding. On the other, when I used a size medium frame for time trials, it actually seemed like the right size as long as I used a longer stem to ensure my knees did not hit the aerobars when pedaling out of the saddle. You know if you have a LBS in your area that sells Giant, maybe it might be worth your while to give them a visit and test ride both a medium and large TCR.
¯\_(ツ)_/¯