To determine the height of the triangular base of the pyramid, we start by recalling that the base is an equilateral triangle with an edge length of [tex]\(5\)[/tex] units.
For an equilateral triangle with side length [tex]\(s\)[/tex], the height can be calculated using the formula:
[tex]\[
\text{Height} = \frac{s \sqrt{3}}{2}
\][/tex]
Given that the side length [tex]\(s = 5\)[/tex] units, we substitute [tex]\(s\)[/tex] into the formula:
[tex]\[
\text{Height} = \frac{5 \sqrt{3}}{2}
\][/tex]
Thus, the height of the triangular base of the pyramid is:
[tex]\[
\frac{5}{2} \sqrt{3}
\][/tex]
Therefore, the correct expression that represents the height of the triangular base of the pyramid is:
[tex]\[
\frac{5}{2} \sqrt{3} \text{ units}
\][/tex]
