Why do my new NiNh batteries drain so quickly in my Minolta DiMage 5 camera?

Rechargeable NiMH batteries tend to only produce 1.2 volts, and as such, won't always successfully power devices expecting 1.5 volts or a multiple of such. It could be that your rechargeable batteries are losing voltage too quickly, whether they can still provide power or not, and falling below the threshold for that particular electronic device, or perhaps they have been damaged, or aren't being fully charged.
 
I had the same issue with a camera I used to have.
For that camera it seemed like all batteries would die out in about 5-10 pictures, which for brand new alkaline batteries seemed crazy.
BUT!!!...
Check your camera's instruction manual, i would guess that it likely recommends Lithium batteries.
That camera that only took 5 to 10 pics before killing the batteries lasted through hundreds of pics when I used the batteries the manufacturer recommended. I used Energizer Lithium batteries and the difference was night and day.