5.8 miles is a good run, but doing it to the gym and back means you're doing 11.6 miles everyday (if you attend the gym everyday). I run to mine which is about 3 miles and run back, go to the gym every other day, and ride a bike to the swimming pool in between!
One of the causes of shinsplints can be overstriding, and suffering from the impact, especially if you're not used to running much, or you up the level you do. Also, poor running technique. People do say that running on road transfers more of the impact up your leg, as opposed to running on grass, which is a little bit softer. Up to you to decide which is best for you.
If you have built up slowly to your 40 plus miles a week you will probably be fine. If you have gone from running ten miles a week to that I reckon you'll burn out pretty soon due to over training. However as you are only 22 or so you can probably get away with it a lot more than some one in their early thirties!
For me 15 miles a week is about my limit I make the rest up on the bike & swimming.