I am using my iPhone 14 pro for 5 month and battery health goes to 97%. I can replace and check it under warranty?

See this excerpt from the "Your battery's maximum capacity" section of the support article: iPhone Battery and Performance - Apple Support

"A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge." In other words, if maximum capacity is below 80%, the battery is below normal performance. You can still use a device with a lower health percentage than 80% but for optimal usage you may wish to consider having it changed when it reaches 80%.

Batteries are consumables and 1-2% loss per month is perfectly normal. According to iPhone Battery and Performance - Apple Support , Apple apparently only considers it unusual (and warrant-able) if a battery drops below 80% maximum capacity in less than a year after you receive it. Ergo, some storage loss as you use it is expected and acceptable. Incidentally, that possible 20% drop over the first 12 months equates to 1-2% drop per month being within the range of what Apple finds acceptable.

The battery is fine. It’s normal for rechargeable batteries to lose battery health with time and use. About 1% per month is average. The drop is not linear.

The battery needs to be replaced when it reaches 80%

Battery Health is an inexact figure that varies with useage. Yours is excellent! The average Apple Battery lasts for two years. When Battery Health reaches 80%, it will be time to make an appointment at the nearest Apple Store for Battery Replacement. In the meantime, check out this link...

Batteries - Maximizing Performance - Apple

Things like battery degredation is normal and isn’t covered under warranty.