I decided to dabble in hyperfactorials for a change and, well, first off, 5 tetra-factorial is pretty big. Approximately E2.188#(E3.339#4). I approximated this as E3#4#2, although I'm not sure if this is as accurate as is attainable. It's pretty close, though, I think.
I'm also working on approximating 6 tetra-factorial and 7 tetra-factorial. Googologically speaking, tetra-factorials are pretty weak, but pretty interesting, too.