Currently Being ModeratedApr 21, 2013 2:06 AM (in response to koukst)
Sounds like you have a home button fault as both symptoms relate to the home button, e.g. Siri is normally activated by holding the home button. Screenshots are normally taken by pressing the sleep/wake button and the home button together so then you are switching on the phone it probably assumes the home button is also being pressed and takes the screenshot.
You will need to make a Genius Bar reservation at your local store and take it in. They are able to replace the home button module on the iPhone 5 which is most likely what they will do. Just ensure you have a backup in case they do decide to replace the phone.