Find a vector function that represents the curve of intersection of the cylinder $\displaystyle x^2+y^2=16$ and plane $\displaystyle x+z=5.$

I am stuck. I setting the equation equal to eachother but i could not solve for anything or get anything useful out of it.

I believe I am supposed to project the cylinder down so its a circle on the xy plane and then find the ellipse that the intersecion makes but i cannot figure out how.

Any help would be appreciated.