Given the figure above, if a = 5.53 cm and b = 4.15 cm, what would be the force (both magnitude and direction) on the 5.0 nC charge?

its a rectangle with + 10nC top left, -10nC top right and 5.0 nC bottom right.

figure? is a the top dimension? b the height, if so...

force of repulsion then is ...
let x,y be directions up, and to the right (for vectors).

F= k( +10nC)(5nC)(y/.0415^2 + x/.0553^2) + k(-10nC)(y/.0415^2)

I assume you know k from Coulombs law.
so do the math, then sum the two y components, remember this is force of repulsion, so it should be downward, and to the right (ie, +x and-y directions)