The situation is shown in the above picture.
From definition:
[tex]\tan (angle)=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]From the picture:
[tex]\begin{gathered} \tan (55)=\frac{x}{350} \\ \tan (55)\cdot350=x \\ 500\text{ ft = x} \end{gathered}[/tex]Then, the height of the building is 500 + 5 = 505 ft
