You shouldn't have an issue with an HE washer. The length of pipe sounds a bit long though. You might be able to get away with it since it's 4-5 feet lower, but not sure. I have "T"ed off more times than what Art recommends in his book with success, so his 100' recommendation might be conservative, but it still sounds a bit too far away. No difference, though, in the set up. It works on the pressure generated from the pump, which is still strong enough in an HE washer.
Also, you shouldn't be using greywater in a veggie garden (you just said "garden" so I'm assuming you meant veggies). You should only be irrigating perennials with it.
