Q: is the new operation system ios 10 supporting iphone 5

Yes it works on the iPhone 5. Your iPhone needs to be restored. It went into recovery mode if you are seeing the connect to iTunes screen.

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

iPhone

• iPhone 7
• iPhone 7 Plus
• iPhone 6s
• iPhone 6s Plus
• iPhone 6
• iPhone 6 Plus
• iPhone SE
• iPhone 5s
• iPhone 5c
• iPhone 5

Hello Osmanov

Yes Apple IOS10 supports all devices from the iPhone 5 and forward.

Meaning, iPhone 4S is not included in the update.

Best Regards

Klas