To find the building's elevation above ground, we first need to determine the height of the building that is above ground.
Given that the basement is 15 feet below ground, we can denote the height of the building above ground as \( H \).
The total height of the building, which includes the height of the basement and the height above ground, is given by:
\[ H + 15 = 70 \text{ feet} \]
To isolate \( H \), we subtract 15 from both sides:
\[ H = 70 - 15 \]
\[ H = 55 \text{ feet} \]
Therefore, the building's elevation above ground is \( \boxed{55} \) feet.