I just looked up the 2011 Trek 520 on Bikepedia (
https://www.bikepedia.com/Quickbike/...spx?item=22633) and it says the bike came with Avid SD5 brakes and Tektro RL340 levers. Strangely, these products are not compatible with eachother - the levers are road-style 'short pull' levers and the brakes are long arm 'long pull' brakes.
I find it weird that Trek would have been including this setup in 2011... The result of this mismatch has been known since 1995 (dawn of the V-brake era) - the brakes have to be set extremely close to the rims, and even when set extremely close will possibly still rub on the rim, especially after a few years when the brake cable is not performing as new, and especially on the rear which is more susceptible to problems caused by cable friction. When everything is perfect, the brakes might work ok, but with very squishy lever feel and potentially requiring too much lever movement.
Possible solutions:
1. Replace levers with 'long pull' levers - Tektro RL520 is the long-pull version of the RL340.
2. Replace brakes with 'mini-Vs' - shorter arms on mini-Vs require less cable pull than long armed brakes, and so will work with short pul levers.
2.a (edit) Replace brakes with centre-pull cantilever brakes. Canti brakes are trickier to set up, and require cable stops on the rear brake bridge and fork crown. Canti brakes are compatible with short pull levers.
3. install Travel Agents (
https://problemsolversbike.com/produ..._agents_-_6416) to multiply the cable pull from the short pull levers. I find these very ugly, but they are effective, especially if you have other limitations like combined brake/shift levers that are only available in short pull, and/or have tires too big (or tires and fenders) to fit short-armed mini-Vs
4. Replace al cables, remove brakes and clean and lube pivots, true wheels to as close to perfect as possible. This may or may not be an acceptable solution, and even if it works it will go back to rubbing and feeling squishy as soon as the cables wear a bit and the wheel gets a bit of runout.