To find the area bounded by the parabola, tangent, and coordinate axes, we need to find the points of intersection of the tangent and the parabola.

Finding the Equation of the Tangent:
The slope of the tangent to the parabola at any point (x, y) is given by the derivative of the equation of the parabola. The derivative of y = x^2 - 1 is dy/dx = 2x.

Using the point (2, 5), we can find the slope of the tangent at that point:
dy/dx = 2(2) = 4.

So, the equation of the tangent can be written as y - 5 = 4(x - 2), or y = 4x - 3.

Finding the Points of Intersection:
To find the points of intersection, we need to solve the equations of the parabola and the tangent simultaneously.

Substituting the equation of the tangent into the equation of the parabola, we get:
x^2 - 1 = 4x - 3.

Rearranging the equation, we get:
x^2 - 4x + 2 = 0.

Using the quadratic formula, we can solve for x:
x = (4 ± √(16 - 8))/2
x = 2 ± √2.

So, the points of intersection are (2 + √2, 5) and (2 - √2, 5).

Finding the Area:
To find the area bounded by the parabola, tangent, and coordinate axes, we can divide the region into two parts: the triangle formed by the tangent and the coordinate axes, and the region bounded by the parabola and the tangent.

1. Triangle Area:
The base of the triangle is the x-axis and its height is the y-coordinate of the point where the tangent intersects the y-axis. Since the y-coordinate is 5, the area of the triangle is (1/2) * 5 * (2 + √2 - (2 - √2)) = 5√2/2.

2. Region Area:
The region bounded by the parabola and the tangent can be found by integrating the equation of the parabola from the x-coordinate of one point of intersection to the other. The integral is given by:
∫(2 - √2)^(2 + √2) (x^2 - 1) dx.

Evaluating the integral, we get:
[1/3 * x^3 - x]_(2 - √2)^(2 + √2).

Substituting the values, we get:
[1/3 * (2 + √2)^3 - (2 + √2)] - [1/3 * (2 - √2)^3 - (2 - √2)].

Simplifying the expression, we get:
(8√2 + 2 - 8√2 + 2) = 4.

Total Area:
The total area bounded by the parabola, tangent, and coordinate axes is the sum of the triangle area and the region area:
5√2/2 + 4 = 37/24.

Therefore, the correct option is (c) 37/24.