Power Supply for Arduino on breadboard (ATMEGA328PU) from a car battery
Instead of using a Linear Voltage Regulator like the 7805, I would recommend you to use a buck-boost module for providing a stable 5V to the Arduino as the linear regulators are inefficient and waste a lot of power in the form of heat.

As @Mattman944 said in comments, adding a fuse will prevent things from getting haywire in the case of a fault in wiring.

Also, you can just get a USB car charger (like this one).