Sorry if I didn't make myself clear, but you got it anyway
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I was speaking from the general in the first paragraph to the specific (your case) in the last. So yes, what it comes down to is the approach you described. EXCEPT, I didn't mean when you stall. I meant if and when you find that no PR's are not being made. So this approach is for if that happens before you stall.
If you wait until you stall then I doubt very much that approach would work. But if you continue to make PR's for the most part but stall out on the 5x3 then the best approach would going straight to 5x5 with a back off in weight to build up for a few weeks. If you stalled on the 5x3 and just switched off to the 5x5 (even with adding reps for two weeks to get there) I don't think you'd progress as far.
I think this set-up has become a "produce weekly PR's" thing instead of a progression thing for many. Let's not forget the main way to get stronger...simple progression (as simple as you can get away with) and THAT is the best way to produce those PR's.