Why does Lincoln face right on the US 5 dollar bill?

Despite many internet rumors about why the portraits on US Coins and bills face a particular direction, it's purely artistic license.

The portraits are generally inspired by paintings or engravings, so whichever direction the individual faced there is simply reproduced on the coin or bill. For example, the famous Lincoln penny was designed by the sculptor Victor D. Brenner. He had already created a medal honoring Lincoln, and he merely modified the image slightly to adapt it to the front of the cent.