How to change modified date in a node when users votes more than 5 times?
Since vote_up_down uses voting API underneath, you can use the voting rules module to allow you to configure rules to fire when votes are made.

You could then make a rule that fires when a vote is made, that then checks the total number of votes for that node and if it has 5 votes update the nodes updated date and save.

So the event/trigger would be voting on the node, the condition would be that the node has 5 votes (after a quick look it is likely the "Evaluate the results of a vote on a ..." condition), and the action would be updating the modified/updated date of the node.