Find the height

$\tan54=\dfrac{x}{500}$ $\implies$ $x=500~\tan54$

$height=500~\tan54+5=$ $\boxed{693.19}$

Shelia is standing 500 ft away from the base of a building.Her eyes are precisely 5 ft above the ground. From this point, the top of the building makes an angle of 54 degrees with a line parallel to the ground. How tall is the building?

Draw the picture. You have a right triangle with base = 500 and base angle = 54 degrees.

Equation: tan(54) = (height of bldg - 5)/500

(height of bldg -5) = 500*tan(54) = 688.19 ft height of bldg = 688.19+5 = 693.19 feet