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iMore Question unable to download ios update on my new iPhone 5s
Welcome to iMore! Make sure you have enough storage space left on your device by going to Settings > General > Storage > Storage & iCloud Usage. Keep in mind, if you try to download and install an iOS update over the air and don't have enough available storage you should be getting a message indicating a lock of available space.
Regardless, your best option may be to connect to iTunes and update your iPhone that say. Here's an Apple Support article to walk you through the process:
https://support.apple.com/en-us/HT204204