The linked Wikipedia page references a OOPSLA 2005 paper by Matthew Hertz and Emery D. Berger that presents data saying that with 3x memory you might reasonably expect a 17% slowdown when compared to manual memory management. (And 70% slowdown when limited to 2x memory.)

Of course there have been some advanced in GC technology since 2005 (and that paper was deliberately measuring a relatively standard generational approach). But I don’t think I’d call the 5x figure a serious exaggeration.

Yes I've read the paper. Advances in CPU microarchitecture alone have noticeably shrunk that gap. There have also been significant algorithmic advances in GC. For instance, a few simple prefetching hints speed up marking easily by 30%, and parallel marking scales almost linearly with core count, to mention but two simple performance improvements.

So like I said, maybe in 2005 a 3x memory overhead only incurred 17% slowdown, but 3x overhead is at least at par, and possibly even a little ahead, of manual memory management.