Shimano 105 brifters - rear shift jumps multiple gears
Often, this is a problem with derailleur adjustment, so I'd double check and triple check that first.

The first thing to do is check if the rear derailleur is bent. If it is, get it un-bent - it is near impossible to adjust a rear derailleur which is bent adequately. The second thing to make sure you have adequate cable tension, proper cable installation and your derailleur is adjusted properly. Here are some good directions on doing that (as well as here). 

Assuming your cables are installed properly and you've adjusted your derailleur correctly (and as correctly as possible) and your chain+cassette aren't worn, then I'd start by replacing the rear derailleur (you may have developed a lot of play in it, and it is significantly cheaper than a shifter) and then look into replacing the shifters.

IIRC, the Shimano 105 shifters from about 10 years ago were shoddily built, so it may be the shifters after all.