The surface area of a solid cylinder can be calculated by summing the lateral surface area and the areas of the two circular bases.

1. Lateral Surface Area (LSA):

The lateral surface area of a cylinder can be calculated using the formula \(LSA = 2\pi r h\), where \(r\) is the base radius and \(h\) is the height.

Given \(r = 4\) cm and \(h = 5\) cm:

\[LSA = 2\pi \cdot 4 \cdot 5 = 40\pi \, \text{cm}^2\]

2. Area of Each Circular Base:

The area of a circle is given by the formula \(A = \pi r^2\).

Given \(r = 4\) cm:

\[A_{\text{base}} = \pi \cdot 4^2 = 16\pi \, \text{cm}^2\]

Since there are two circular bases:

\[2 \cdot A_{\text{base}} = 2 \cdot 16\pi = 32\pi \, \text{cm}^2\]

Now, add the lateral surface area and the areas of the circular bases to get the total surface area:

Total Surface Area = Lateral Surface Area + 2 × Area of Bases

Total Surface Area = \(40\pi + 32\pi = 72\pi \, \text{cm}^2\)

So, the total surface area of the solid cylinder is \(72\pi \, \text{cm}^2\).