Personally I would not make any drastic changes.
Of all the lifts, the overhead press increases the slowest, so what you're running into is pretty normal.
One of the ways you can get stronger is to accumulate volume at lower intensities than your current RM.
So lets say your current 5RM is 40k, and you're currently trying to increase that to 45k. If you get more volume in at 40k and 42.5k, using sets of 5, that will usually drive your 5RM up. Once your 5RM is 45k, do the same with 42.5k and 45k, and get it up to 47.5. Etc.
One of the ways to accumulate volume is to use backoff sets. This lets you see how close you are to a new 5RM, and still get the volume in the same session.
After warming up with lighter weights, do a set or two near your 5RM (you might get 3 or 4 reps), then back off 2.5-5kg and do sets of 5 with that. A 5x5 isn't a bad place to start for a backoff set, but you can increase the sets or decrease the rest times. Just work in increasing your work sets over time until you hit 5 with your top set. Then increase and repeat.
Another way to accumulate volume is to do it by waving the intensity by repeating prior sessions. So, with 5x5. 35, 37.5, 40, 37.5, 40, 42.5, 40, 42.5, 45, etc. You can do 2 steps forward, 1 step back; 3 steps forward, 2 steps back, or whatever. There's lots of options.
The first time you get the 5x5 with a heavier weight, the reps probably aren't going to be very clean. The next time you do those same weights, you can work to improve your form, the quality of those reps, the speed of those reps, or the rest times between. Eventually you will "own" a certain weight for a 5x5, and that also means you're stronger.
Yet another way to accumulate volume is with the "+" sets that TrevorLPT mentioned. When you deload, just work on setting rep PRs at the lighter weights.
In the end it's these are all pretty much the same idea: you push forward and test out a new weight, and then do more or less work with lower weight until you can do more next time. There's a bit more going on with 5/3/1, but it, too, follows this same principle.
I also recommend 2.5kg jumps instead of 5kg jumps... but 5kg can work. The amount of time and work it takes to add 5kg to your PR is going to be about the same, no matter how you do it. The biggest difference is that it's nice to hit a new 5x5 PR sooner, since the next weight up is closer.