Prepare your body for the volume of running in tournaments and practice.
Ultimate players can cover multiple miles over the course of a tournament weekend. For a starting player I estimate they cover between 8,000-12,000m through 8 games (40-60 points, with ~200m per point). That's 4000-6000m/day. This is based on personal observational and case study experience. There isn't any ultimate running volume data I find convincing in research journals.
I'd consider it unsafe to train for, or train at, the volumes some players experience at tournaments. I've heard of college players playing 90+ points at a tournament. That's dangerous. Period.
So, based on those volume *assumptions*, we can cover 5-7.5 miles/tournament.
In your off-season/pre-season training you need to get close to the volume an athlete would experience in one day of a tournament.
Let your practices/alactic conditioning prepare you for the high intensity volume of tournaments.
What about those 3-5 mile distance runs?
12,000m = 7.5 miles
6000m/day = 3.75 miles/day
Ok, so if I need to build up to that distance, why not just use long slow distance runs? Reread that wording again. Long SLOW distance (LSD). Most of ultimate is walking, running at ~70% speed, or moving at high intensities. Although you'd be meeting the distance guideline you'd be preparing in a way that doesn't match the demands of the sport. LSD helps develop aerobic fitness, but there are more specific methods.
I suggest using Tempo Runs as your primary method for developing aerobic fitness. Tempo running, following the Charlie Francis High/Low methodology, involves running at or below 75% intensity (speed) for that given distance interval. Rest periods can vary from 90s for starters to 30s for elite athletes, and the shorter the interval the shorter rest time needed. Avoidance of lactate buildup is key (that heavy, fatigued feeling in your legs). Here is an example, called the "Big Circuit" ala Charlie Francis.