You won't kill yourself but you might kill your core's VREG. Typically you'd wanna feed it with 7V - 10V. If you have a heatsink on your 7805 and preferably no CS this might well work, but the 7805 will get pretty warm. What you can to is to put an 7809 (+ caps) in between the +12V and J1 of the core. Grounds go together. Do that as close to the psu as possible and only once (star-wiring).