There is really no limit on where the price will go. It could take 20 years, but I don't think $5000 per bitcoin is impossible. In fact, we've already seen the price go over $1000 a couple of years ago.
back then there were much less coins in circulation, plus there was a massive amount of hype as bitcoin made it to news channels world wide. the rising price attracted so many yolo investors that the price kept going up till the bubble exploded. don't forget the mtgox bots that were constantly buying up the price. we don't have all that right now.