I know this is a bit of a necropost, but it seems there's some new, old stock V5's going around. I bought 2.
I figure some more people are going to look at this.
The Nokia BL-4c is 860 mAh, 53 x 34 x 4.5 mm. The original is 60 x 44.5x 3.6 mm
The Nokia BL-4u is the closest match at 1000 mAh, 61 x 38 x 4 mm
The battery door will not close with either of these batteries, even with the controller physically disconnected (as it is in the plastic shroud at the top of the battery) and the label removed.
If you find a compatible battery and the controller is giving you trouble, you can "trick" the device.
Above information is from
here
Of course, all experimentation is at your own risk.
I believe the 4c and 4u works as is, with the existing controller, but I could not confirm that.
I am actually still using the original battery, which I do want to replace as it is probably unsafe.
I did find the exact battery for sale in Russia, I asked them if they were willing to ship it, they simply told me it was not possible.