people you're size can bench 250, but only if they have very short arms, and/or have been lifting pretty seriously for awhile, and/or are naturally quite strong, or some combination of these. I don't know your arm length, but since you don't seem to have the 2nd two characteristics I mentioned (lifting for awhile, naturally quite strong), it is quite doubtful you will be able to approach this amount any time soon.
But it also sounds very unlikely that your friend will be able to approach a 5 minute mile ( unless he runs a decent amount or is a naturally great athlete who does decent cardio) . If he is like most meathead lifters, he won't be able to approach 6 minutes.
So you will both lose, meaning no one will lose: a draw. (you could do a tie-breaker: whoever, in 2 months time comes closest %-wise to the goal. In other words, if he runs 5:30, that is 110% of the goal (divide actual performance by goal performacance). You'd have to lift about 225 to match him. If he runs 6:00, you'd have to bench 210 to just beat him. Maybe THAT is your answer, and you will both get in better overall shape.