Here's the general information about how to make biodiesel:
Welcome - Collaborative Biodiesel Tutorial Website
Get started by making some 1-liter batches first so you don't mess up your 5 gallons.
Then, if you're really stuck on making only 5 gallons and don't want to make a fullsize processor, there are two options:
-make two 2.5 gallon batches by shaking a 5-gallon jug (like oil comes in) with pre-heated oil and methanol/lye in it. It'd be just an upsized version of the 'Dr Pepper' method that's outlined in the starter articles at biodieselcommunity.org. You can preheat the oil in a large pot on a hot plate or on the stove if it doesn't smell too badly.
-or, if you want to use a 5 gallon 'reactor', perhaps you could do this:
use an air-powered drill and a paint stirrer to stir a batch in a large bucket with a lid on it (the stirrer will just go through a small hole in the lid). DO NOT, under no circumstances, DO NOT use a regular electric or cordless electric drill for this, as the sparks from the drill could cause an explosion (and that has happened to several people who have used drills to mix biodiesel). An air-powered drill is only $25ish dollars from harbor freight tools, Tractor Supply Co, WalMart, etc, and it does not produce sparks at the 'processor' area.