From experience
It needs to have a valid MOT and then needs to go for a VIC check.
When you apply for a V5 the DVLA will send you a letter saying car is registered to you but that to obtain a V5 you need to complete a £38 VIC check first.
Take car to nearest VOSA centre and it takes about 15minutes. Then they give you a letter and mark it on the dvla computer and you can re-apply for free from the V5.
The V5 will show thats its been a damaged repaired vehicle.