Can I actually profit from bitcoin mining on my PC? My PC is kind of power hungry but it's also quite powerful too I was wondering if I might be able to profit from bitcoin mining without a mining rig, even if the profits are small.

Relevant Specs:
GPU: AMD RX 480
AMD: FX 8320e
PSU: 450w Thermaltake 80+ Bronze PSU
OS: Ubuntu 16.04 LTS
You definitely will not make any kind of profit, even if you had free electricity. The chances of bitcoin mining frying your computer are higher than the chances you make enough bitcoin to pay back a new one.

Bitcoin mining used to be done on CPUs and GPUs (6-8 years ago, not sure on the exact time range), and later was done on Field-Programmable Gate Array (FPGA) miners, which are more powerful than CPU and GPU mining. In 2013 the first Application-Specific Integrated Circuit (ASIC) miners were created, and these are created for specifically mining bitcoin. I would highly recommend against mining with your CPU, as you can't compete with the ASIC miners. I wrote a bitcoin mining guide here (archived) which explains a bit more about mining and discusses why you shouldn't mine with a PC. However, as I lay out in the article, I definitely think you should buy a small, inexpensive ASIC miner to learn more about bitcoin and mine a few bits because I think it's a fun and informative hobby.