Your goal is to accelerate the particles to kinetic energy k. what minimum radius r of the cyclotron is required?

Considering the magnetic force is providing the centripetal force,

we get, mv^2/r = qvB

so, r = mv/qB

as the Kinetic energy, K of the particle is given by. 5mv^2

so, v = sqrt (2K/m)

substituting the in radius equation,

r = m*sqrt (2K/m) / qB

r = sqrt (2Km) / qB