I'm starting to train on a 8 lane, 400 meter track at a local stadium. Unfortunately, I can only use lanes 5-8. I was wondering if there is a simple equation to determine how many laps in lane 5 one would have to run to equal 1 mile. I'm sure there is an equation for this, but I'm running out of brain cells. Thanks!

Measure the 2 turn stagger out another 3 times for that lane. This would give you an "8 turn" stagger and the eqiv. of mile in lane 1.

1600 or True mile?
 

Brian's suggestion will work perfectly for a 1600m workout.
If you really want a true mile, then deduct 9.35 meters from your "8" turn stager point.
1 Mile is 1609.35 meters.