Can this be solved with any HP CAS?

[AlexFekken]

Yes, domains matter: in the compactified complex plane, i.e. on the Riemann sphere, 5 is a (the) valid solution for the equation. No ifs or buts.

Arguably the Riemann sphere is the nicest and most natural domain to do calculations in (and to do function theory on), so in that sense I applaud Skynet's choice of domain :-)

Asking ambiguous questions and expecting unambiguous answers is just another case of GiGo. Blame your expectations, not the tool.