Help....whenever I buy salad at the food store it gets slimy within a few days.

Yeah, I can't explain the miracle of the restaurant salad bar greens either. It's possible they are rinsing them in a chlorine solution again, but I rather doubt it. Bagged salads are scary things at best. As long as the bag is intact, the greens inside are living in a special gas bubble that allows them to exclude oxygen and hopefully extend their life. Of course, that also relies on the temperature and light exposure to be correct the entire time- and fluxuations in both DO count against it. So in the loading, offloading, stocking, handling, and then you transporting it home, replacing it in a fridge at what may not be ideal temp, opening the bag and releasing the precious preserving gas- not a surprise it gets slimy so fast. The longest lasting version of any food is the one that is meddled with the least, and is in the closest to it's natural form. So for lettuce, that's in the head or whole leaf- not chopped up and mixed with other shredded/chopped veggies. Not washed in bleach water that's washing who knows how many other heads, bugs, etc, over several hours. The longest lasting salad greens will always be those you buy intact, and store in cloth bags in a properly humidified and temperature controlled veggie drawer of your fridge. Not as convenient, perhaps- but then unlikely to be contaminated with listeria or going slimy and wilted in a day or so.

Doing what wrong?
Can't explain the miracle survival of leftover dressed salad from restaurant, but yes problems with ready to eat eicery store greens in those clear plastic boxes.
These greens have already been washed, and maybe treated with a preservative.
So they've been days in transit, treatment and store shelves by the time you buy them. No wonder they go bad in a day or two. (Aldo sometimes carry disease more readily than raw greens.)
Instead, get unwashed heads of lettuce and other vegetables and prepare salad yourself....use some of the techniques you mentioned like washing and storing in paper towels.

WILTED...not winter