There is no normal reading, it varies greatly amongst diabetics, particularly in the mornings. 5.1 is a good reading, 8 is a little high but remember, these meter readings can be up to 20% out so your 8 may actually be 6.4. There are other factors with morning readings too such as Dawn Phenomenon and Somogyi Effect ( Google them ). Basically, they can both increase morning BG levels.
Ideally, your waking levels would be between 4 & 7. You are not too far off really.