Driving from Split to Dubrovnik

I havent driven that road since the Yugoslavian split into separate nations, but I doubt there is a border stop. Anyway it wont be long if there is one. The road is slow because of lack of maintenance and many curves and small villages.

Driving the road just takes lots of concentration to avoid trouble. And control of speed. Usually there is no shoulder to the road.

We took the road from Split to Dubrovnik twice last month. Yes, there is still a border stop. In fact, you are stopped when you enter the strip of coastal Bosnia- stopped by both the Croatians and the Bosnians- and then you are stopped again when exiting Bosnia & re-entering Croatia. It was pretty harmless, though, but be sure you have all your papers in order.

Does it really take five hours to drive the 125ish miles?

Yes, it really takes that long, maybe even a bit longer if there is much traffic. It's a cliff-top, coast-hugging road with not much opportunity for passing. I recommend taking a bus & there are several throughout the day to choose from. You can just sit back & enjoy the gorgeous scenery.