I've found I can resolve M13 and M3 with a C5 in fairly dark skies if I give myself time to dark adapt, and pump the magnification (15 mm minimum, usually more like my 9.7 mm). Dark skies probably help me, though. Not saying I wouldn't rather look at it through a C8, but I definitely get more than a gray blob out of those two globs if I'm patient and look after my night vision.
Being best obsever you can be with a smaller scope is the best way to be the best observer you can be with a larger scope. It's easy to be lazy with a larger scope, smaller scopes keep you honest.
M13 and M3 are two big bright globular. By my standards, under dark skies a 5 inch will resolve some stars in M13 and M3, a C-8 will resolve more.
In my experience, good seeing or poor seeing aperture is always a help with globulars. A larger scope will show more globulars, will resolve more globulars and will resolve more stars in a globulars. Even in very large scopes, most globulars are poorly resolved. What a large scope does is increase the number of M-13-like globulars visible.
Unfortunately, the seeing will not typically allow that full 60% better resolution. The eye's response is also quite nonlinear, so while the light grasp is indeed 2.6x, it will only appear to be about 37% brighter when looking through the eyepiece (at the same magnification).
So yes, there are advantages to be had from the larger scope, but it's often easy to overstate the real-world impact of those advantages.
I think it's easy to understate the advantages of larger apertures. Make your comparisons at equal exit pupils and the numbers are very different.. with deep sky seeing is much less important.
Look at M13 in the C5 at 125x, the equivalent exit pupil in a C-8 is 200x.
Once I was selling a fairly large scope. The prospective buyer brought along a scope for comparison. The scope I was selling was about 2.3x larger in aperture. The buyer asked if I minded if he set up his scope.. I said no but that one look through the larger scope would be enough for him to realize a comparison was unnecessary.
Indeed, that turned out to be the case. He commented later that M-79 in Lepus in the bigger scope looked like M13 in his scope...