Wow. You might just need more power in general. Let me see...A little thinking out loud....
http://www.tomshardware.com/reviews/radeon-r9-270-review-benchmarks,3669.html
750W needed for the graphics cards alone, though your particular models obviously use more than the AMD spec with a 2 6-pin requirement (seems like they are similar to the 270Xs and not the 270s?). Your other components wouldn't use more than the ~250 left over, but the other rails may require some of that power which reduces that available to the 12V. If you are running close to the PSUs limit, you need to make sure it is a good quality PSU.
That board supports up to 3-way crossfire (in the 2 x16 and 1 x8 slot; the other 2 are 4x which should be fine for mining as well):
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128509R
You can use the 4-pin molex to 6-pin PCIe converters for a couple of the connections.
If you need 10 6-pin PCIe power connectors, your going to have to look at 1500W PSUs or somewhere above 1000W supplies to get the 6-pin native connections:
Enermax Maxrevo 1500W
and that will run you around $450.
Try this with your current supply... Try booting with just 3 270s and see what that gets you. If the PSU still doesn't work with only three GPUs, I'd exchange it. Start there in the troubleshooting. You already know it makes the clicking noise and the fan doesn't run.
Now if it works for three, but it doesn't work when you add the fourth or the fifth, it could be that the PSU is faulty or the motherboard can't operate with GPUs in the x4 slots for whatever reason (power to the slots?).
Most likely, you'll end up exchanging the PSU. If you don't want to get into a $400+ PSU, you'll have to use the 4-pin to 6-pin adapters for a couple of the cards.