I don't know that the excess fluid would leak out of the dipstick tube, assuming it was attached correctly / wasn't damaged. The 4L60 *does* have an overflow tube / vent; it's at the top of the case (so you'd see fluid coming from elsewhere; and depending on 'how much', it could get pretty messy.) Keep in mind that if fluid *is* coming from that vent, it doesn't have to be solely from 'overfill'. But if you're not leaking from there, we won't worry about that, for now.
As for what 'could' happen if overfilled...I don't know every single thing, but there's a seal on the tailshaft that could get blown -- if it does, you'll start seeing fluid leaking from there. Those things can have trouble even when there's *not* too much fluid, so it doesn't hurt to give that a look-see when you're doing your maintenance checks.
If a shop did the trans, I'd definitely stop by. Or, you can drain the pan & refill it with 4qts, check the level for reference, then add the 5th qt (preferably before starting). Note that the level will read high with the engine off - when you start the engine, the fluid should then read lower on the stick.
If you use a clean container, you could reuse the fluid (so it 'costs' nothing except your time / labor). Probably a good idea, when you're draining it, to check the mounting on the dipstick tube, as well - clean it, make sure it's secure, and recheck for leaks afterward. Also, use a container that will hold more than 5qts (just in case).
If you don't have a drain plug (or can't loosen it, indicating that it still might have the factory (over)torque on it), I'd definitely take it into the shop, assuming that you had one R&R the trans (not many here would take on that job themselves)