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Here's a followup mainly to test if I can get the hang of the code entry: The curve $X_{split}(5)$ has genus $0$ and degree $15$, and a Hauptmodul is $s$ where $$j=\frac{(s+5)^3(s^2-5)^3(s^2+5s+10)^3}{(s^2+5s+5)^5}.$$

Secondly the Hauptmoduln for all genus zero $X_0(N)$ are given in the very nice paper by Robert Maier (2008) In fact we derived the one for $X_{split}(5)$ from Maier's for $X_0(25)$.

OK, so there was no code entry after all, but I did get to include a link!