Depends on which GL5 you're talking about. I've run the Valvoline full synthetic GL5 for 20 years and some 150,000 miles in my TR3A diff, with no ill effects. In fact, I credit it with making the diff (which was already well worn when it came to me) live so long.
The GL5 spec says nothing about oil composition, it's only a performance specification. There is a particular sulfur-based additive that some gear oils use to boost their performance, which can break down over time to form sulfuric acid that will attack copper and brass. Even some GL4 oils use this additive (it's the one that gives used gear oil that distinctive stink). But not all oils do.
The trick, I believe, is to look for an oil that is also rated MT-1. MT-1 says little or nothing about corrosion (it's for non-synchronized heavy duty transmissions), but has a long term stability requirement that the sulfur additive doesn't meet.
However, there is another problem with using GL-5 rated oils in synchronized transmissions. The synchronizers operate by friction, and most GL5 gear oils are too slick for good synchro operation.