I couldn't even get away with a soft pad with a foam cushion under it, when I lived on the third floor of an apartment building years ago. 

I'm in a building that was just opened within the last five years and dance games of any variety causes the walls to shake for the apartment downstairs. Unless you're on ground level, it's probably a no go.

If you don't mind sharing the machine, you might have luck getting your apartment building to agree to put it in a common area like a gym, if they have one.

If it is an older apartment made of steel and concrete construction, it MIGHT work if you put 2 layers or more of rubber mats under it.

http://www.sears.com/search=garage%20floor%20rubber%20mats

I only suggest this because most 5 story apartments are NOT wood frame. However, if it is wood frame construction, then you're not going to do it without pissing people off.

Alternatively, when myfriends and I owned our dedicab (but no garages or houses), we chipped in and rented a storage shack for ~$40/month that had an electrical outlet nearby that we could use to play the machine. It's unorthodox, but it did work.

Edit: Buildings in seismic zones sometimes put the building on a series of huge springs to prevent it from vibrating during the quake. In THEORY, I could see something similar maybe being used to support a DDR stage and dampen vibrations transferred to the floor, but it would take a stupid amount of effort to construct such a dampener and I don't even know if it'd work.

http://whitehouse.gov1.info/raven-rock/raven-rock-photos/building-sits-on-springs.jpg

Hmm, it's a pretty new building but it is 7 stories tall, so I don't know about the construction. It's sounding like a common area or storage unit is probably my best bet. Though a spring dampening system is just the kind of ridiculously overengineered solution I like...haha.

Thanks for the input, everyone!