Hi A.,
I realize that you mentioned that you typically make the older one "try" for 5 minutes to play with the little one or just "cave in" and play for a little while, but believe me when I tell you that this is ONLY making the situation worse. I know with 4 kids (especially when two are twins) that it is sometimes easier on you to have your older son entertain the younger one so that you can care for your twin girls. However, the younger brother is learning that if he pesters long enough, he will get his way. And your older son will grow to resent the fact that he feels like he has to 'parent' his younger brother. Your younger son will continue his strategy as long as it is working and he is getting his way, and he is learning that if he is persistent and pesters longer, you will eventually give in and make his brother play with him. Instead, maybe you can teach your younger son ways to entertain himself so that the older brother can get some time to himself. Even kids need time alone.
And if the little one won't cooperate with verbal instruction, then it's time to put him on a 'naughty' mat or take away privileges if he continues to pester his brother about playing with him. He may ask, but if big brother says no, then "no" means "no." Please nip this in the bud now before your little one is disillusioned into thinking he will always get his way in life and become a disruption in school as well.