5 Second count after made hoop
 

Gentlemen:

After a made hoop the new offense picks up the ball, with the clock running, and we begin our 5 second count. Sometimes they don't pickup the ball very quickly, probably because the coach sometimes wants a certain player to make the throw-in or they tap the ball to me, because they don't realize that I don't have to touch it after a made hoop, or whatever reason.
Is it possible for a player to purposely not pick up the ball, keep the clock running and let the game, quarter, half , end.
When or can we start a 5 second count if the player has not picked up the ball.

You start the count when the ball is at the disposal of the throw-in team. Usually that is when they grab the ball and get OOB. If they purposefully try to delay the count, start it when you judge someone from that team could have the ball ready for a throw-in.