The first thing I would do is get an OD pedal in front of it. This isn't as much to add gain as it is to clean up the gain that you're jamming into the front end (frequency shaping, there will be an associated tonal change). Any of the popular OD pedals should work: Keeley modded TS9dx or TS9, MXR GT OD, Maxon TS808, etc. I would buy something used from Ebay, buy a few, and experiment. I keep it on all of the time except when on channel 1 for cleans because it does add some level of grit even with the gain completely off. I've gone through at least 12 OD pedals, and widdled my way down to two, though I'm on the Analog Man KOT order list.
You will also find completely different sound from each power level, and if you have the fx loop on or off. Be careful flipping the fx loop, when off, it seems to disengage the master volume and you will get full bore power to your speakers. As Dave mentioned, mind the bass knob. I'd keep it slightly below or at 10oclock in all situations.
The Mark V isn't complicated, it's just sensitive, but insanely flexible. Mine is for home use only, so I have it set to 10W, fx loop on with a delay in the loop, and an OD pedal and tuner up front. That's it. Be careful with the EQ. Start with a V shape and work your way to the sound that you like. Be patient, you'll get what you're looking for from this amp, I'm sure. Give it at least a few minutes of warm up time as well, not just the 30 secs mentioned in the manual.
Anyway, congrats. You just purchased the only amp you'll ever need. At least until you pick up another Mesa...