Extremely high order harmonic processes are used to generate ultrashort pulses for attosecond physics. I think harmonics up to the 30 or 40 or even 50 range (odd numbers ofcourse) are quite often used to generate attosecond pulses in the extreme UV range.
Specifically fifth order processes, I am unaware of. As far as I am aware most nonlinear spectroscopy or microscopy applications can conveniently achieved in the third order. So, in case you don't have a new scheme, I can't benefits right now.
Even if a fifh order process would be interesting, probably a cascaded second or third-harmonic process will still be more efficient.