I'll have a go... someone correct me if I make a mistake.
basically we're looking at something like this...
You'll notice in the diagram that the angle between the gravitational force acting straight down and the normal force on the block (force due to gravity acting perpendicular to the surface of the ramp) is equal to theta, where theta is the angle of the block with the horizontal.
Another picture to help explain that (if you didn't know already)
So... using these relations (note the first picture) and summing all the forces, we can say...
where 'mu' is the coefficient of friction, 'M' is the mass, 'g' is the gravitational constant, and 'theta' is the angle between the ramp and horizontal
the M cancels out of the equation to leave
g*sin(theta) - mu*g*cos(theta) = M*a [eqn 1]
Looking at the constant acceleration formulas, the best one to use would be
V^2=V_0^2+2*a*(x-x_0) [eqn 2]
where 'V' is the final velocity, 'V_0' is the initial velocity, 'a' is acceleration, 'x' is final location, 'x_0' is initial location
You can see that both 'V_0' and x_0 are zero (starts from rest, and we'll call the starting location zero. You also know 'V' to be 5.25 m/s and 'x' to be 8.35 m from the problem statement. You've solved for 'a' using [eqn 1] and then you can plug 'a' into [eqn 2] to obtain a value for 'mu'.
That's about it... like I said, if I messed something up, someone jump in and save me!