iPhone 5 won’t restart on holding both buttons My iPhone 5 froze after the YouTube app failed to open.

I've tried holding the sleep/wake button + home button down with no luck. Nothing happens. I'm able to slide down the Notification Center and type and search in the box but then I try to open an app and nothing happens.

If I press and hold to activate Siri, she appears for a second then turns off as if I pressed the home button again.

I've tried connecting the iPhone to a Mac but as it's passcode enabled it tells me to unlock it and then replug it which I'm not able to do.
If Siri starts but then stops "as if [you] pressed the Home button again", I'd say there might be a problem with your Home Button. Try using the Apple earphones with volume/play control and use that to press Home button for Siri. Does Siri still behave the same way?