To calculate the emf (electromotive force) of a material with a given flux density and area, we can use Faraday's law of electromagnetic induction. This law states that the emf induced in a closed loop is equal to the rate of change of magnetic flux through the loop.

The formula for calculating emf is given by:
emf = -dϕ/dt

where emf is the electromotive force, dϕ/dt is the rate of change of magnetic flux, and the negative sign indicates the direction of the induced current.

Given that the flux density (B) is 5sin(t) and the area (A) is 0.5 units, we can calculate the magnetic flux (ϕ) by multiplying the flux density and the area:
ϕ = B * A

Now, let's find the rate of change of magnetic flux by taking the derivative of ϕ with respect to time:
dϕ/dt = d(B * A)/dt

Since the area is constant, we can treat it as a constant and take it out of the derivative:
dϕ/dt = A * dB/dt

Differentiating the flux density B = 5sin(t) with respect to time, we get:
dB/dt = 5cos(t)

Substituting this value back into the equation for the rate of change of magnetic flux, we have:
dϕ/dt = A * dB/dt
= 0.5 * 5cos(t)
= 2.5cos(t)

Finally, we can calculate the emf using the formula emf = -dϕ/dt:
emf = -2.5cos(t)

Therefore, the correct answer is option 'D', which is 5cos(t).