Car rental is cheaper than tours, but you learn SO much more in Iceland with a tour. We've been there 4 times so far and always rent a car but plan at least one tour on each trip.
For 5 days in July I'd rent a car but take a Golden Circle tour with a minibus or superjeep provider so you're not stuck with the issues a big bus always presents. Then drive the South Coast and Reykjanes Peninsula. Try to get lodging for one night along the south coast so you can get all the way to Jokulsarlon.