To find the work done by the winch, we first calculate the force exerted by the winch. The force required to pull the load up the plane includes overcoming both the gravitational component along the plane and the constant resistance.

The gravitational force component along the plane is given by:

\(F_g = mg \sin \theta = 50g \sin 60^{\circ}\)

Substituting the values, we have:

\(F_g = 50 \times 9.8 \times \sin 60^{\circ} = 50 \times 9.8 \times 0.866 = 433.0 \text{ N}\)

The total force exerted by the winch is the sum of this gravitational component and the constant resistance:

\(F = F_g + 100 = 433.0 + 100 = 533.0 \text{ N}\)

The work done by the winch is the product of this force and the distance moved along the plane:

\(\text{Work done} = F \times d = 533.0 \times 5 = 2670 \text{ J}\)

Thus, the work done by the winch is 2670 J.