Using a PIC to perform switch on and timed shutdowns in automotive environment
You can use 7805's this way, but as they only replace one resistor (and require 2 additional decoupling capacitors each!) I would never do it this way. My suggestions:


replace the two 'sensor' 7805's by resistor / zener-diode combinations. Use 4v7 zeners.
add two 100nF capacitors at the input and utput of the remaining 7805
add a suppressor diode over the relays coil!!
I am not sure a jellybean 7805 is a good idea in an automotive environment, there can be nasty spikes on the power line.