Going to $5K doesn't mean anything, certainly not the start of a bull market. That could just be the top of long term trading range or the top of a bull trap. See November 2014 for a potentially similar move. People will think it's the start of a bull market and then get bull trapped.
It's possible, but people seem to be so focused on their perfect chart bottoms, that they might get trapped in themselves. Back then we had nothing going for us while today that's different.
On the other hand, currently it seems that we're stuck below the previous resistance around $4200 which might indicate that the little bit of momentum we had is fading. Typical bear market behavior that is.
Regarding OP, this could very well turn out to be a very long lasting bear market. Higher prices means more money needs to flow into Bitcoin in order sustain the current levels.
Based on that it's difficult to say, but my best guess would be $2000-$2500 assuming the bottom isn't in yet.