How much would a used i7 6xxx series CPU cost you? I'd hesitate to advise a jump from 2 cores/2 threads to 4 cores/4 threads when many games already can use more than 4 threads.
Which brings us to the games you play. If you play quad core CPU demanding games, yes a move to the i5 will be worth it. If you play games that aren't using your current CPU to 100% usage, then the i5 probably won't make as big a difference as you hope. If you play, or intend on playing, the newest and most demanding games then the i5 is not enough.