The more normal approach is to use a buck converter, often followed by a LDO regulator. You're asking the 7805 to drop a minimum of 7v with the engine off, The car's 12v can go up to 14v or more with the engine running, so consider the power dissipation at that voltage, and it can spike much higher than that because you can get a "load dump" when systems are switched off, which momentarily pushes the voltage right up. So you're better to drop some of that voltage in an efficient way. Buck regulators are easy to build..Depending on the system you're designing you might want to just build a 5v buck, or you might want go a bit higher and stick a 5v linear regulator on its output, which gives a cleaner supply.
In a car you've got alternator noise and a load of other noise on top of that. It's typically all fairly high frequency. Depending on how noise-sensitive your application is, I'd go with the manufacturers recommendation for the regulator I was using (typically a ceramic cap close to the regulator, and an electrolytic one. You can add extra filtering if needed.