<p>This paper investigates the finite and infinite propagation speeds of solutions to a fifth-order Camassa-Holm (CH) type equation. This equation can be regarded as a generalization of the CH equation in a geometric setting. Although the conclusions for this fifth-order CH equation are similar to those of the classical CH equation, the methods of proof differ substantially. The proof of infinite propagation speed for the CH equation depends critically on a strictly positive definite integral quantity related to the solution <i>u</i>, this property that no longer holds for this fifth-order model. To overcome this, we establish a corresponding non-negative integral quantity and combine it with the decay properties of the solution to derive the desired results.</p>