Hi Richard, Your catenary should not be directly earthed in normal circumstance, in fact it is considered good practice in industry to insulate one (or both) ends with porcelain or nylon spacers, this is not normally required in a domestic situation. There are two issues with standard Cat5 cable that you may wish to address:- 1) The outer insulation is thin and any movement relative to the catenery wire (e.g. in windy conditions) is likely to abrade the sheath. 2) Because the outer insulation is thin it's exposure to UV light is going to embrittle the sheath quite quickly. Therefore it's important to source cable with a black sheath (high carbon-black content) to minimise the effect.
If your span is not excessive, running the cable(s) in conduit may be more suitable.