I believe that it will hit 5.000$ in a really short period of time before going down to 1.800-2.000. To prevent the network from stopping I think that some governments/banks might start building huge mining farms to keep the network alive, much against the idea of being decentralized though
So you mean to say that bitcoin will touch the price of $5k directly from and then it will fall back to $2k? And if you feel so then your statement doesn't make any sense as there is no scope that bitcoin can achieve that high price in this quick time.
If it starts a parabolic rise then 5k$ is achievable in a matter of weeks, remember bitcoin has been through such rapid price rises several times in the past.