What are the PSU specs; How many rails; what brand; how old is the PSU?
If it is sold on Newegg provide a link.
What motherboard will they be run on?
Do you have a wattage meter like, Kill-A-Watt brand?
In the mean time, here are some helpful articles.
The 5850 has a maximum board power of 151W to 179W, depending on model.http://www.guru3d.com/article/radeon-hd-5850-review-crossfire/2
We'll now show you some tests we have done on overall power consumption of the PC. Looking at it from a performance versus wattage point of view, the power consumption is pretty good for a product of this caliber, according to ATI the 5850 has a TDP of 151 Watts.
Keep that in mind. Our normal system power consumption is much higher than your average system.
System in IDLE = 168 Watts
System with GPU in FULL Stress = 348 Watts
(5850 consumption = 180 Watts)
Recommended Power Supply
So here's my power supply recommendation:
Radeon HD 5850
The card requires you to have a 500 Watt power supply unit at minimum if you use it in a high-end system. That power supply needs to have (in total accumulated) at least 40 Amps available on the +12 volts rails.
Radeon HD 5850 CrossfireX
A second card requires you to add another 170 Watts. You need a 650+ Watt power supply unit if you use it in a high-end system. That power supply needs to have (in total accumulated) at least 55~60 Amps available on the +12 volts rails.
For each card that you add, add another 200 Watts as a safety margin.
Single GPU 5850http://www.guru3d.com/article/his-radeon-5850-icooler-v-turbo-review/6
System in IDLE = 157 Watts
System with GPU in FULL Stress = 334 Watts
Difference (GPU load) = 184 Watt (official reference TDP = 170W)
Both models did draw 180 Watts+, but in mining power consumption can be less depending on how you clock your cards so working with a wattage meter will provide much better info.