With our dry conditions, you don't have to worry much about fungus.

You can always set the timers for something like 1 AM instead of 5 AM. The main thing you want to do is make sure you're done watering before it starts warming up.

Another thing I would suggest is that if you have areas that don't get enough water with that schedule, or maybe the sprinklers don't reach some spot very well, instead of running the sprinklers longer or more often, take the hose to those areas. There's no need to water the whole lawn just for a small section that dries out sooner (although that seems to be a concept foreign to many in my neighborhood).

Watering with this schedule will help your grass put down deeper roots. After watering on this schedule for a while, you might try to see if you can cut back to watering once a week, but for a longer period at each station (change 8-12 minutes to 12-16 minutes). You'd be applying 1.5 times as much water per station, but only once a week, so you'd be using 3/4 the amount of total water.

A "rumor" I heard, probably on here somewhere, was that plants are open to receive moisture during the cycle when there is moisture in the air that typically settles as dew in the morning. Also that as the day gets warmer, plants start reacting to heat by closing up to retain moisture. You may notice this on plants whose leaves appear to droop to retain moisture. The thought was that if you water late in the night or early in the morning, you would benefit the landscape's regular cycle rather than try to convince it otherwise. My personal thought is that you should observe your landscape regularly so you would notice whether you are having sprinkler problems (such as a water fountain that you did not install) before things die or yellow significantly. Whether this happens by observing the effects of watering or during the watering process is up to you.