You don't by any chance have one of those cheap third-party battery grips attached to the camera? They have their own on/off switch and battery (obviously) and when such a grip is attached and active the switches on camera can sometimes behave differently than you might expect.
Also do you have the intervalometer switched on? Or is there an IR remote somewhere near your camera that is accidentally being pressed and switching your camera on? Or is your TV remote or some other IR emitter in your house activating your K-5?
The other possibility is that your K-5 has a virus or backdoor inserted by some intelligence agency who wants to monitor you
Anything is possible nowadays.