I want to requlate a 15Vdc down to 5Vdc, should I just use LM7805? or should I just use LM317? what is the advantages and disadvantages of each IC to each to one another?
Your choice. LM7805 will need less external components. LM317 will ask for external voltage divider. If you are drawing considerable current, you will need to fix a heat sink. I prefer LM317 because I do not need to stock all the different ones...
Both seems fine.. If you don't want to use any external components on basis of calculations, Just go for 7805... If you need more operating current you may need to use LM317. Any way in both the cases you need to use heat sink as you are going to waste more power.
Unless you need current greater than 1 amp, use the 7805. it requires less components. If you use a 317, you'll need an adjustment pot, or precision resistors to set the divider to 5v.