5cm is large - but the chance of cancer is still about 20%. It should be removed, but if the opposite lobe has no nodules, then the initial surgery could be a lobectomy -- but if it's cancer, then a completion thyroidectomy will necessary.
PET findings for follicular lesions have been inconsistently helpful -- some studies suggest if it is PET negative, it is less likely to be cancer, but other studies suggest PET cannot predict cancer at all in these cases.
If possible, send the slides to a university (ie U Penn, Hopkins, U Florida) to make sure they agree it is indeterminant and needs to be removed. The size alone, in some experts' opinion, suggests it should be removed.
There is currently no way to predict CA confidently enough in these cases, and removal is the standard of care.