Some comments on the hints (too bad this little coda spoils the joke at the end of the previous paragraph, but it really doesn't belong anywhere earlier in the answer):
"Knowledge of demonology might be useful": I guess we're looking for a 5-letter or 10-letter demon name. There are lists all over the internet. "Knowledge of the alphabet and a wheel might be useful": I took this to indicate that we're doing some sort of code-wheel thing, or equivalently moving letters around mod 26. (Or maybe mod something smaller than 26 if we're using a smaller alphabet.) "Arithmetic and eros": not sure what this is about, other than that again it might indicate that we're adding or subtracting those numbers to get letter values. There is a journal article, or book, or something, called "The arithmetic of Eros", apparently about the Song of Songs in the bible and the poetry of Sappho, but I don't think that's relevant. "Clocks" again suggests modular arithmetic; perhaps it specifically suggests working mod 24, as we would do with an alphabet where I=J and U=V or with the Greek alphabet. I have re-checked the results of adding and subtracting (both ways) mod 24 and translating either into an I=J/U=V Latin alphabet or the Greek alphabet, and I don't get anything sensible.
Another thing one could try, I guess, is
to add up the numbers around each of the five larger outer regions, and see whether that gives anything useful. I get, clockwise from just right of the top, 38 32 18 19 25. Mod 26 that's 12 6 18 19 25 = L F R S Y, not obviously useful. Mod 24 it's 14 8 18 19 1; with the shortened Latin alphabet that's O H S T A; with the Greek alphabet it's X TH S T A. If either of those is the name of a demon, I don't recognize it.
Perhaps
there's some traditional way to do letter-arithmetic to pentagrams, but if so my cursory investigations haven't found it.