I have no experience with the D5100 but I would be very confident that the two displays should be the same if they are in fact meant to be measuring the same parameters.
If the two readings are not made essentially exactly simultaneously then it is possible for a number of factors to influence the result. In low light conditions a very small change in the degree of obstruction of light from a stronger light source can make a noticeable difference in exposure. The act of moving one's head or arm or body even slightly may be enough to change readings depending on how far away the target was and the relationship of light sources.
In extreme cases, light entering via the viewfinder when your eye is not blocking it may cause the LCD reading to read as if there is more light on the subject than is actually there.
If it is not possible to read LCD and viewfinder values simultaneously by yourself you could use two people with one calling out the reading for the other person to confirm.
If the readings do differ under such controlled and simultaneous conditions then it suggests either that the camera is faulty (which seems unlikely) or that the two displays have somewhat different intended purposes (which also seems unlikely:-).