Its ok to charge iPhone 13 pro with 5 w

Yes. It will however take a very long time to charge, and if being used while charging, may not actually charge and even loose charge, but no damage will come to the iPhone by using a 5 watt charger if that is really what you want to do.

No, using a higher power source will not damage the battery, because the charger in the phone regulates the energy to the battery. See→Fast charge your iPhone - Apple Support

Specifically:

Fast charging works when you use an Apple USB-C to Lightning cable and one of these adapters:

• Apple 18W, 20W, 29W, 30W, 61W, 87W, or 96W USB-C Power Adapter
• A comparable third-party USB-C power adapter that supports USB Power Delivery (USB-PD)

Yes it will work but it will take a loooong time

I recommend you try and 20w charger

https://www.apple.com/shop/product/MHJA3AM/A/20w-usb-c-power-adapter?fnode=64893510ae20c0800b9dadeb3b908f43f54f15c5bade249f2506cfe7521bb04616b5f65834db9c1b70ff4c38ac3fe6362f58054103c1d80e1d5e511c3e29349edcb0e11e24a0f20e3d27057e0ec8fb3a35d38d89ea0f3febf1adf25bf22e1f77e2a1c98fe6c416cd7a697e2d064089dc&fs=f%3Diphone13promax%26fh%3D458e%252Bf658c9

Iafeef wrote:

Yes the maximum limit is 20 watt

There is no maximum limit on the power source. The most it can use is 20W, but it can get that from a 91W power source if that is what you have. The charger is in the phone, and only takes what it needs from the power source.

I know that, but I think using a adapter with a capacity of more than 20 watts may cause damage to the phone's battery.

Yes the maximum limit is 20 watt

No, it won't.

It will not. Assuming the correct output voltage, the rated power could be 1,000,000 watts and the phone would still use only the power required.

Thank you very much for this valuable information.

and thank you stedman & kurtosis This is the best place to learn a lot about products 

Agreed, I come in here all the time to learn.