@cola nice to see someone wanting to get after it.
I skimmed the advice above.. I agree with some of it... I think? Most of it I don't but whatever here's mine.
Two things that I recommend:
1. Pain is not solely due to poor form. This is outdated and it's more complicated than that. For example, just the preconception itself that benching causes shoulder pain can cause shoulder pain. Because your brain is sending a signal, pain (a protective mechanism), to be cautious of that area even if it isn't hurt. I'm not saying it isn't, but I'm saying it's more complex than just bad form. If you would like to learn more about pain and why it's happening, I would suggest checking out Barbell Medicine (a group of strong ass medical doctors) and visit a physical therapist.. maybe even one of Barbell Medicine's therapists. They have a lot of content explaining pain. Ultimately, I recommend a good PT. They also have a free beginner routine. Which leads me to my next point.
2. If you want to get good at bench pressing.
Bench press more. Powerlifting is really big on specificity. You want to do movements that are similar to the one you're trying to improve I order to get it stronger. 5x5 is an okay program. But it is also outdated. At the time it was released, 5x5, the Texas method, and 5/3/1 were free templates you could get online. That was huge a decade ago. But now there are much better programs online.
Like this one. The reason those programs aren't great is because they don't consider periodization, fatigue of the athlete or any other factors that are important for long-term gains. You can run those programs, and you will make some progress. But you may stall. You may even injure yourself. For example, earlier this year I injured my adductor while squatting 330 lbs doing 5x5. I went from 275 to 330 in a month and my body was not ready for that load so quickly. 5x5 doesn't have periodization (I'd suggest googling this, I've already typed too much here and there's many articles that would explain it better than I). So boom, injury. Now I have a coach and things are much better. I just squatted 330 for 5x5 easy earlier this week. Anyways, fvckalldat. I just realized when skimming through the Beginner Prescription on BBM's website that they offer 60 pages of info on why their program is the way it is and have videos (including a 17 minute bench press video) at the bottom on how to do the major lists. Damn if I didn't have a coach you already know what I'd be on. Doing accessory movements will not improve your bench press as fast as bench pressing and doing other press variations will. Obviously some accessory work is needed but after the main lifts. Powerlifting (or moving heavy weight in general) is more than moving weight, it is a skill. You have to learn how to brace, leg drive, keep a tight upper back, break the bar... All at once. I mean you don't have to, but you'd move bigger weights if you did.
I guess it helps to have some credibility with these kind of things so for that sake: I weigh 195 lbs. I've only been bench pressing since I started with my coach 5 months ago. I was doing 155 lbs for 5x5 in week 1 to drill the technique. Yesterday I was doing 230 for 4x5 and I recently hit 280 lbs for 1 after 3x3 with 235 lbs.
If you have any questions lm happy to chat about it or try to help find an answer. Wish you the best in your journey, get that sh!t.
"Big back, big bench. Big back, big total."
I have long arms. 6'1" height. Who cares if long arms makes it harder. Just get that work.