I've worked on multiple Poulan Pros over the past year or so and... hated them all. I currently have a 5020 in the shed that was near new, and I picked up for a
very good price along with another smaller Pro (I forget which model, 3816 I think) and they didn't really have anything seriously wrong with them. They were garage queens, still in the carrying case, with the typical carb/fuel line nonsense, so I did muffler mods and tunes, and what I really hate about them is that they're so @$!#ing erratic to tune. Along with the pull start - they never feel like they have any compression...
I got the 5020 running reasonably well, and had a friend use it to help me cut up a sizeable oak that went down (> 20" trunk), so it's definitely capable of doing some work, but they're just... I dunno, quirky, finicky, odd saws and they don't feel like they have a lot of grunt for their cc's. Maybe I'm just biased toward the old saws, but I was running a 10-10 and a Super-XL on this same oak and I just smile all day long running those animals! Loud and gutsy (yes I know, a few more cc's) and never give up. They'll also shake you like you owe them money LOL. I can't even really say I hate "plastic" saws either, I love my 455 Rancher.
Not a Poulan hater either - I had a Farmhand 2900 that I patched up and sold, and I kinda regret it now, that saw would get it, even with a 20" bar and full comp chain! I'd take that over a 5020 any day.
Suggestions above are a good place to start. Muffler mod helps and makes it sound more like a real saw.
I use a dremel with a burr to open everything up, just make sure you get the filings cleaned out so they don't backwash into the cylinder. Retune (open up the high needle a bit) after that mod.
Clean the carb out, they do seem to clog/gum up easily as MacAttack stated. Run it dry when you're done so you don't have to clean it out next time hehe. Take your time and adjust in small increments. Typically saws will start/run enough to get a good tune with 1&1/2 turns out on both needles, but the 5020 likes it a little juicier as I recall. I want to say 2-2&1/2 out on both as a starting point. It might say on the saw if the sticker is still there. Should "four stroke" no-load and clear up under load. If you've ever watched a Buckin Billy Ray video, you can clearly hear his Mac(s) burble when he lets up and then they just hum when it gets back in the cut.
Not tryin' to piss in your cheerios with my Poulan angst either, hope that saw works out for you! Good price for it if it's a runner and gets the job done. I'm giving mine to my brother-in-law until I can finish the 10-10 I'm building him.