Solution:

Given:
- Area of the isosceles triangle = 12 cm^2
- Length of one of the equal sides = 5 cm

Formula for the area of a triangle:
- Area = 1/2 * base * height

Calculating the height of the triangle:
- Let the height of the triangle be 'h'
- Since the triangle is isosceles, the height will form a right angle with the base and divide the triangle into two equal right-angled triangles
- Using Pythagoras theorem, we can find the height:
h^2 + (1/2 * base)^2 = (5)^2
h^2 + (1/4 * base^2) = 25
h^2 + 1/4 * base^2 = 25
h^2 = 25 - 1/4 * base^2
h^2 = 25 - 1/4 * base^2
h^2 = 25 - 1/4 * base^2
h^2 = 25 - 1/4 * base^2
h^2 = 25 - 1/4 * base^2

Calculating the base of the triangle:
- Area = 1/2 * base * height
- Substituting the values of area and height into the formula, we get:
12 = 1/2 * base * h
12 = 1/2 * base * sqrt(25 - 1/4 * base^2)
24 = base * sqrt(25 - 1/4 * base^2)
Squaring both sides to eliminate the square root:
576 = base^2 * (25 - 1/4 * base^2)
576 = 25 * base^2 - 1/4 * base^4
576 = 25base^2 - 1/4base^4

Solving the quadratic equation:
- Rearranging the equation in standard form:
1/4base^4 - 25base^2 + 576 = 0
- This is a quadratic equation in terms of base, you can solve this using the quadratic formula or factoring.

Therefore, the base of the isosceles triangle is approximately equal to the value obtained by solving the quadratic equation.