Hardly anybody would recommend 5x5 these days for anyone, much less beginners.
* Not enough volume
* Non-periodized
That first bit means different things at different phases of a lifting "career". But generally speaking "time under tension" and research into effective rep ranges has changed modern thinking on set sizes and volume.
These days people, including World's Strongest Men, tend to recommend higher rep ranges for beginners and those coming back to the gym to build work capacity and reduce risk of injury.
For reference, I went from a dumbbell bench press of 45lb to 75lb in 4.5 months (5x5). Previously my progress was much slower.
I'll caveat that I've obviously not closely controlled for all factors and I'm an n of 1. Additionally my interest is in having a great strength to weight ratio, rather than being a body builder. I'm a climber and that's an important consideration.
Progressive overload works. Those programs "work".
They are just out of vogue for beginners, and they are both targeted towards beginners.
You have been lifting weights somewhat regularly for 25 years, majority 3x8-12, and the switch to 5x5 increased your dumb bell bench press from ~20kg to ~35kg?
There is just no way. That is extremely light weight. Like, most beginners who follow any sort of progressive overloading system will be at that level in 4 weeks starting from essentially 0
after 15 years of lifting, I'm currently pushing 4x10 with 50kg dumbbells on the bench. So yeah, 35kg after 25 years seems odd unless those 25 years weren't exactly "serious" or "consistent" let's say.
No judgment, but yeah
That's why I recommend keeping it simple. Build the habit and build some strength. Once you've done that, you can get fancy if you find that you're really into it.
What are your goals?