How to put ringtones on my iphone 5c without using itunes

There are several methods to put ringtones to your iPhone without iTunes:
Method 1: Put custom ringtones to iPhone via GarageBand. Transfer your desired music from streaming platforms or cloud servers to GarageBand. Then apply it to ringtone after trimming it.

Method 2: Purchase directly on iTunes store. Or redownload purchsed ringtones via same Apple ID.

Method 3: Transfer downloaded ringtones from computer to iPhone directly. Make sure the downloaded ringtones are in m4r format. If not, you can modify them directly before transferring.

Here are two tutorials for your reference:
https://www.digitaltrends.com/mobile/how-to-make-ringtones-for-iphone/
https://www.leawo.org/tutorial/how-to-add-ringtones-to-iphone-6.html?qa=1409

Navigate to part 2 in this guide, and you'll find out another practical way to transfer ringtones to iPhone instead of using iTunes: https://bit.ly/3ecH907
Hope this helps!

It's very convenient to transfer ringtones to iPhone via iTunes. If you don't want to use that, you'll need an alternative. I'll recommend you this iTransfer tool. It can be helpful for the data transfers of iPhone, iPad and iPod among iOS devices, iTunes and PCs.

1. Run the iTransfer after installing it on your computer. The software will indicate that it's now safe to connect the iOS devices. Then connect your iPhone to computer with the USB cable. It'll automatically detect the device, and then show the libraries of your iPhone in the left sidebar.
2. You are allowed to drag and drop the ringtones into the window of the software to start the transfer. Or you can click "File" at the upper right corner and then choose "Add > Add File/Add Folder" to add ringtones from computer.
3. The ringtone transfer starts immediately after choosing files. The dialog of transfer process will pop up, and the progress bar will show the percentage of the transfer process. After the transfer, the ringtones will show up in your iPhone.

There are lots of apps on the App Store that enable you to use songs as your ringtone if thats's what you mean?