A few notes:
20% charge wouldn't be 5 volts as that would be dead, dead, dead - way below 0%
Modern multistage chargers can show a constant 50-70% charge for a long time (hours) during part of the charge regime. I've seen mine at 67% for hours, then finally go on up to 100%. At only 2 amps it could take quite a few hours to get past that plateau.
I would think a new battery should be well above 20% charge when you buy it but I have no idea how well these stores maintain them.
Again, the battery age parameter in the car has to be reset or your new battery won't be charged properly.