How to transfer data from this phone to iPhone 13 ?

Dear Gona981,

First of all congrats on the upgrade :)

There are 2 ways you can transfer your data from an iPhone 5 to an iPhone 13.

The first one is to make a iCloud backup. Go to Settings > iCloud > iCloud backup (the settings might be called a bit different, I cant recall the exact names because I haven't used that version of iOS for a while). Ones you made a iCloud backup you can start setting up your new iPhone. Make sure to log in with the same Apple ID as your prevous iPhone to select your iCloud backup.

For more details on the first method, check out this Apple Support article: https://support.apple.com/en-us/HT210217?cid=tw_sc_icloud_092421

The second way is to make a backup on a Mac or PC (PC using iTunes). Check this video out on how to make a backup on a Mac:

https://www.youtube.com/watch?v=JNSbVc11Yn4

Ones you did this you can start setting up your new iPhone, and select the "Move data from Mac or PC" tab when asked on how to set up your new device. Plug in your new iPhone into your Mac or PC and select your previous iPhone from the menu bar.

Check out this article for more details on the second method: https://support.apple.com/en-us/HT210218?cid=tw_sc_icloud_092421

Lastly, this is the Apple Support article to get all the info you need plus all the info above: https://support.apple.com/en-us/HT201269?cid=tw_sc_icloud_092421

Hope it helps :)

Actually, the best way is with Quick Start, described here→Transfer data from your previous iOS or iPadOS device to your new iPhone, iPad, or iPod touch - Apple Support and also demonstrated in this video:

Dear Lawrence Finch,

Are you sure that Quick Start is available for the iPhone 5?

To my knowladge the iPhone 5s is the oldest model to support this feature in iOS 12.something.

You are correct! My error; I didn’t see the iPhone 5 post, I responded to the OP. However, the link still covers other methods.