The magnetic part using the Lorentz force is: F = q v x
B, 
where v and B are vectors and v x B is the vector cross product. 
Magnitude of the force: F = q v B sin(α) 
So, sin(α) = F/( e v B), with e the proton charge. 
This will give you a value for sin(α), and two potentials
for its opposite.
You will now look for: 
sin(α) = 7.40 10^-13/( 1.60 10^-19 * 5 10^6 * 1.78) 
= 0.520
So either sin(α) = 0.502 or sin(α) = -0.502 
The 1st α = 30.1 degrees or α = 150 degrees. 
The 2nd α = 210 degrees or α = 330 degrees. 
So we can say that 30.1 degrees and 330 degrees would be minimum and biggest on [0,360]