Calculate Surface Area of a Cube with 5 cm Edges: Geometric Problem

To determine the surface area of the cube, we will follow a systematic approach:

• Step 1: Identify the provided information.
  The edge length of the cube is given as $5$ cm.

• Step 2: Utilize the formula for the surface area of a cube.
  The formula is $6a^2$, with $a$ representing the edge length of the cube.

• Step 3: Substitute the given edge length into the formula and perform the calculation.
  Using $a = 5$ cm, the calculation becomes:
  $6 \times (5 \, \text{cm})^2 = 6 \times 25 \, \text{cm}^2 = 150 \, \text{cm}^2.$

The computed surface area of the cube is therefore $150$ cm².

Therefore, the correct choice among the given options is the fourth choice, which is $150 ~cm²$.