Hi thisarafrommatale,
Thanks for using the Apple Support Communities. If you are trying to restore your iPhone via Recovery mode and are having issues with it timing out after 15 minutes due to a slow download, you may find the information and troubleshooting steps outlined in the following article helpful. In particular, this section would appear to address the specific issue you are describing:
4. When you see the option to Restore or Update, choose Update. iTunes will try to reinstall iOS without erasing your data. Wait while iTunes downloads the software for your device. If the download takes more than 15 minutes and your device exits the connect to iTunes screen, let the download finish, then repeat step 3.
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If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support
Regards.
