There are a number of viruses that are never flushed out of the body and they remain in the body after infection. In certain conditions they can manifest years after the initial disease has passed. But that is very rare. Flu viruses, RSV are not able to linger in the body.

If symptoms re-emerge days (5-6 days tops) after the initial symptoms have gone away, then either the body hasn't really recovered from the infection or it's another type of infection on top of the initial viral infection (bacterial infection of the upper respiratory system.or maybe even in the lungs for example) or it wasn't a cold from the get-go, it was a cold-like infection.

So best to talk to a doctor.