iPhone charger

Hello,

Yes, a 5 watt charger will work just fine if you use a corresponding USB to lightning cable.

However, to use the USB-C cable that came with your phone, you should get an adapter similar to this one:

20W USB-C Power Adapter - iPhone Accessories 

This option will also give you the benefits of fast-charging. See this:

Fast charge your iPhone

Good luck.

You can use the 5W power adapter and cable from an older device. Apple encourages it. See the following from Buy iPhone 13 and iPhone 13 mini - Apple

As part of our efforts to reach our environmental goals, iPhone 13 and iPhone 13 mini do not include a power adapter or EarPods. Included in the box is a USB‑C to Lightning Cable that supports fast charging and is compatible with USB‑C power adapters and computer ports.

We encourage you to re‑use your current USB‑A to Lightning cables, power adapters, and headphones, which are compatible with these iPhone models. But if you need any new Apple power adapters or headphones, they are available for purchase.