I bought an iPhone 14 Pro five months ago and now the battery is 97%. Is there a problem with the battery????

A 97% Battery Health is good, consider the battery is a consumable so it will wear out , Apple replace it when it drops below 80%. Even if you bought the iPhone 14 PRO five months ago, it depends when has been manufactured and how long was sitting in the shop before beign bought. So no problem with the battery

No, nothing is wrong. Normal war and tear due to usage. Batteries do not be to be replaced until they are below 80%.

You might want to follow these tips.

Batteries - Maximizing Performance - Apple