To find the instantaneous power delivered by a force, we can use the formula:

$$ P = \vec{F} \cdot \vec{v} $$

where $ P $ is the power, $ \vec{F} $ is the force vector, and $ \vec{v} $ is the velocity vector of the particle.

In this question, the force exerted is given as a constant $ 5 \, N $. Since no direction is specified, and the displacement is given in a scalar form, we assume the force acts along the direction of displacement. Therefore, we can treat the vectors as scalars for simplicity.

The displacement of the particle is given by:

$ x = 2t - 1 $

The velocity, $ \vec{v} $, is the derivative of displacement with respect to time. Deriving the displacement equation with respect to time $ t $ gives:

$$ v = \frac{dx}{dt} = \frac{d}{dt}(2t - 1) = 2 $$

The instantaneous power can now be calculated as:

$$ P = F \cdot v = 5 \times 2 = 10 \, \text{Watts} $$

Thus, the instantaneous power delivered by the force at any time $ t $ is $ 10 \, \text{Watts} $.

The correct answer is Option A: 10.