If you think about the forces which are acting, you have weight acting downwards and the 'net' force which is causing the acceleration acting in the direction of the motion of the skater, the yo-yo will want to stay doing what it is doing due to inertia.
If you draw a vector diagram, you will have something like the following:
So, therefore, you can just use trig to solve:
tan (theta) = o/a = ma/mg
tan (5) = ma/mg
Tan (5) = a/g [m's cancel]
a = gTan5
(assuming on Earth, where g=9.8)
a = 9.8 * Tan(5) = 0.86ms^-2 opposite to the direction of the angle subtended to the vertical.