This sounds like a grounding problem to me.
The first thing I would try is to make sure you've got the DS5 connected to AC at the same outlet as your amplifier. This means that you plug your amp and the DS5 into the same power strip or splitter, and that you don't plug the DS5 into a power strip that's plugged into another power strip.
What's going on here? When you get noise like this it may be because the ground level of the AC isn't the same at the two outlets. If there's any difference between the ground levels, then you may get some AC current leaking across the grounds which is the hum you hear.
The DS5 will be particularly vulnerable to differing ground levels because the outputs are unbalanced (2 conductors). It looks like a direct box, but it's just a power supply and connectors. A direct box sits in between two AC powered devices and can have this problem as well, but the balanced connector separates the signal hot, signal ground, and the shield. If you have this hum problem with a direct box, you disconnect the shield connector on one end (that's what the ground lift switch does) and the signal continues to pass on the center conductors, but the hum that was passing through the shield is interrupted. You can't have a ground lift switch with the DS5 because the unbalanced connectors combine together the signal ground and the shield - disconnect it, and you won't get any audio.
So, you need to make sure that there's no ground differential between the DS5 and your amp and the problem should go away.
Many power strips have surge protectors in them. The surge protector circuit isn't supposed to change the ground level, but I'm supposed to have a private jet and it didn't work out that way there either! In the digital world, a lot of errors like the surge circuit don't matter - your phone charger will work if you give it almost anything. But the DS5 lives in the analog world which literally is all black magic and it totally intolerant of close enough.
The giveaway on this problem is that your rig hums when the DS5 is plugged in but the 5-pin jack is not connected. With no input, this must be a leaky ground problem.
If you're already on the same power strip, then the AC filtering circuit in the DS5 has a problem - either one of the big filter capacitors has gone bad or the diode bridge has failed. It's kind of funny that you mentioned about rectifying the problem - this is section of the circuit is known as the rectifier - how come I'm the only one laughing here? (ha - I know Ron just chuckled too!)
David Fung