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I have a 5 year old well established reef tank and I am starting up a new tank. Would it help the cycling process to use the sponge filter media from the old tank.
Definitely - the new would be effectively cycled - though you should monitor ammonia/nitrite the first week after adding fishes. Also i would not move the seeded material until you are ready to add at least a few fishes since the bacteria needs ammonia to stay alive. You will likely see a spike in the 0.5 range and if it concerns you can put in a few drops of sachem prime or equivalent.
Fish would be good - esp something disposable like a guppy or tetra and monitor the water the first week - do not add shrimp they are far more sensitive and even a tiny blib can kill them - also they don't produce enough bio load to be interesting.