Can I run Cat-6 in conduit with line-level power cables?
Barring you bother to source high-voltage rated Cat5e or Cat6A, sharing a conduit with line voltage is a clear and blatant code violation. It's got nothing to do with nails. You should have put in two conduits, or three to cover the unknown next thing. Cat5e will carry full gigabit the same distance that Cat6 or 6A will.
If you are committed to a cable solution, &quot;all dielectric&quot; (no conductive members) fiber optic would be the best choice and code compliant.
Either type of cable needs to be wet-rated as all exterior conduits are wet by definition (and in reality.)
Your least expensive effective option would be a pair of high-quality 802.11ac point-to-point links if there is a clear line of sight from the building with networking to the gazebo.
You could also try a pair of those &quot;powerline ethernet adapters&quot; but I can't say I recommend them.