There is technically no recommended age for a child to undergo surgery for snoring! What is most important is to have the child properly examined to find out why he is snoring, assess how severe the snoring is and finally, how badly it is affecting the child.
The concern is that your 5 year old may be suffering from a condition called paediatric obstructive sleep apnea due to his enlarged adenoids and tonsil tissue. This means he may not be breathing adequately at night while asleep so that there may be abnormally low dips in his oxygen saturation levels. Often children at this age may also suffer allergic rhinitis leading to enlarged turbinate tissue which blocks their nose further.
If anti-allergy meds haven't helped, then I'm afraid the best way forward is probably to have surgery to remove the adenoids and tonsils and shrink the turbinates to help your child breathe better. Tonsils can't gorw back though there is a tiny 0.5 % chance the adenoids may rarely grow back. The turbinates may swell up again in future too if the underlying allergy problem isn't treated properly. Make sure your child gets an allergy test too.
However, please take note that every child is different and therefore should be assessed carefully. I think it would be extremely helpful for you to read the following informative link on common childhood conditions.
