  We construct rogue wave solution of a fifth-order nonlinear Schr\"odinger
equation on the Jacobian elliptic function background. By augmenting Darboux
transformation and the nonlinearization of spectral problem applicable for the
fifth-order nonlinear Schr\"odinger equation, we generate rogue wave solution
on two different periodic wave backgrounds. We analyze the obtained solution in
detail for different eigenvalues and point out certain novel features of our
results.
