Your plan looks solid. I'd keep the rocks, media, and crushed coral wet the entire time since that's where most of your beneficial bacteria live. The same bucket is fine as long as nothing can shift around and damage the corals. I'd keep the fish in a separate bag or small container rather than with the rockwork. It's less stressful for them and there's no risk of them getting pinned if the rocks move. If the drive is only a few hours, don't worry too much about using all new water. Reusing some of the original tank water is fine, but fresh, well-mixed saltwater is perfectly acceptable too. Once you're there, get the heater and flow going before adding the fish back. I'd also keep a bottle of bacteria and an ammonia test kit handy just in case, but with a 5-gallon tank and a short move, you should be in good shape if everything stays wet and temperature stable.
