In general, a "proper" length rear axle will be 11 mm longer than the OLD, leaving 5.5 mm sticking out beyond each locknut. However, that 5.5 mm isn't sacred and the 2.5 mm you have will be sufficient. In fact Sheldon Brown had an article where he said that actually nearly zero protrusion would be ok since the wheel is really held in place by the pressure of the qr skewer. Here is his take on it:

"Axle Length
Typical quick-release axles are 11 or 12 mm longer than the spacing of the hub locknuts. This gives 5.5-6 mm of axle protrusion on each side. You don't actually need nearly this much, so for respacing hubs to wider spacing, if you're not adding more than, say, 5-6 mm of spacers, you don't need a new axle. As long as you have 2 or 3 mm sticking out on each side, that's plenty.
One of my own bikes is set up with the axle cut off flush with the locknuts, and even this is no problem in use, though it is slightly trickier to align the wheel when installing it. See my page about my fixed-gear mountain bikes."