98 Sable Bucks when A/C is on

My '98 Mercury Sable had been running ok until the Extreme Heat has started! It had been bucking, but I changed the fuel filter last fall and it helped, but now it's back! And it is TOO HOT to not be able to run the A/C!
Would a new battery help (mine is almost 5 years old)?
Thanks for any help!