You will need to either use a hardware approach (multiple computers) or a software approach (something like IS Boxer, HKN, Octopus, AHK, Keyclone etc).

I've gone the software route, but there is a hardware forum if you are inclined to use multiple computers. Depending on the strength of your computer, five accounts might be smooth or choppy; you can test how well they will run with trial accounts.

I'll recommend starting with IS Boxer, because it is very simple to use thanks to the wizard. It gets you a strong auto assist option (FTL), the ability to broadcast mouse clicks (Ground Target AoE's), instant swaps between toons and a lot of advanced features which let your software to do more as your needs grow. There is a 7 day free trial.

To play 5 accounts, you'll need five wow accounts.
I'd recommend going with RAF (Recruit a Friend), from your account management page.
A chain is probably the best method, for a starting boxer:
A -- B -- C -- D -- E