How can I switch power between two hard drives using transistors?
Your circuit concept is starting in the right direction but it requires some important changes for it to work.

You will require series base resistors for all of the PNP transistors. As drawn you will cook them with no base current limitation. 

Secondly the NPN transistor is drawn backwards. Its emitter needs to connect to the GND.

Third you need to do some serious work reorganizing the way the bases of the various transistor are biased. You need to separate the 12V and 5V PNP bases so that the 12V one can shut off when the base drive goes away to the 5V one. After this fix it is necessary to provide also a separate pullup of the NPN transistor.

Don't cringe. Resistors are incredibly cheap.

Lastly this schematic, to be bluntly honest with you, is horribly drawn being that it does a bad job of following conventional standards for how a good schematic is drawn.