It would be pretty hard to make OGL 4e products since so many of the terms that are used in 4e don't exist in the SRD. Push, pull, slide jump to mind, and that, right there, would make doing an OGL 4e product pretty tricky.
5e doesn't use a whole lot of new terms, although the terms might be defined differently. So, you can use the OGL with a 5e product, without too much of a language issue.
Those terms are vague enough that you could do it. "Hit Points" and "Armor Class" are less vague. In fact, I'd bet that those terms are OGC somewhere. It seems unlikely that all those years of OGL content could have developed without something called a "push" or a "pull" being in there. But I don't think you'd need those to be in there; they're not unique enough.