I remember the broom exercise at school. Funny, isn't it? Big strong lads can't do it for more than 45 seconds. I thought I'd try it myself given that I'm not 12 any more. I got bored after 5 minutes. Sure, my shoulder aches a little bit, but I reckon I had another 10 minutes of holding my arm out, stock still.
Same here. I'm in terrible shape, haven't been to the gym in over a year. Picked up a broom just now and held it at arms length with one hand out to the side for 5 minutes, which seems long enough to prove the point.
As a teenager I heard a similar challenge involving holding the empty hand horizontally at arms length for five minutes. After 25 minutes without the slightest tiredness I got bored and quit. I figured I was just too skinny or something -- twiggy nerd arms must be easier to hold up than big muscly jock arms.
I'm pretty sure this "can't hold arm straight out for n minutes" is pure myth. Strange that so few people actually bother to try it.