High nitrate does not bother platys, there have been tests done showing that it does not bother them up to 3 or 4 hundred ppm. 5ppm is nothing. However I would suspect that there is a possibility there is something wrong with your tests.
5ppm of nitrate is very low. It does not take very long for nitrate to build up to a high level in such an overstocked tank if the biological filter is processing all of the fish waste. I would suspect that due to the overstocking the filter cannot cope and is not processing all the ammonia and nitrite, which is why we're not seeing the level of nitrate I would expect. What tests are you using? If you are using the strips they are basically useless, totally inaccurate, loads of things will send the results out and they don't work really anyway.
This is definitely columnaris and it needs antibiotics. I don't know what's in the med that you are using but the only thing I have ever found useful on advanced columnaris is antibiotics. You can use just about anything - tetracycline or oxytetracycline (sometimes sold as oxytet), erythromycin, kanamycin, streptomycin, chloramphenicol... almost anything.
Most of the fish in your photos have an emaciated appearance and I'd put money on them having a heavy load of internal parasites. This is very common in livebearers - I actually worm my livebearers as regularly as I worm my cat because it's the only way to stop them being infested. It's even more common when the tank is overstocked and it tends to progress faster.
Here's what I would do. Do your best to get rid of the columnaris. Be aware that doing so will probably kill off your biological filter. Once the fish are healthy, return them to the LFS. You can't keep the plec and clown loaches in that size tank anyway so I'd just keep a few of the platies. Re cycle the tank - you could even return all the platies and fishless cycle. Then work out what you want to keep and how many fish you can have. Treat any fish you have kept from now with worm medication before adding new fish.
Columnaris is a [insert profanity here]. It's an awful disease, I really hope you get through it. Good luck.
