I do both, upgrade LR and upgrade PS.
LR adjustments are exactly the same ones you can do in the Camera-Raw plug-in in Photoshop which you’d be doing if you shoot raw-format photos, but unlike Bridge/ACR is much more efficient for 100s or 1000s of pictures. LR has other functions that photographers might use like uploading galleries or geotagging or printing picture packages, or making photobooks using a specific vendor (Blurb), but LR does not have the layering or precise-selection tools you would use for head-swapping or adding areas of arbitrary text which aren’t what you do in the Camera Raw plug-in, just inside Photoshop, itself.
You can use a newer LR to drive an older PS one photo at a time, using LR’s Edit in PS with LR Adjustments right-click command, and have both sets of functionality having only paid extra for LR. I almost always just use LR and rarely have to Edit in PS, nowadays, but I don’t slice and dice my picture content, either.
If you upgrade computers in the future and haven’t kept your PS-CSx current (upgrade your CS5 to CS6 in this case) and something in your older version of PS isn’t compatible with your newer computer, anymore, then you’d have to buy PS at the full-price—you can’t skip upgrades, anymore.