This is good illustration.
Notice, the water content stays the same; but RH varies with the temp.
I think 5% diff in RH per 1° F sounds a bit much, but there could be other factors.
Edit:
did some calculations
From a starting RH of 65%, at the difference between 71-70 °F, the RH will vary by about 2.1% RH given all other conditions remain same.