What is the area of a triangle where every side is 5 units long correct to the nearest unit?

Since every side is 5 units long, this is an equilateral triangle with side length $s = 5$ units.

The area $A$ of an equilateral triangle is given by the formula:

Substitute $s = 5$:

Rounding to the nearest unit, we get:

The area of the triangle is $\boxed{\text{11 units}^2}$.

From the image, we have side $AC = b = 5$, side $BC = a = 6$, and the included angle $\angle C = 60^\circ$.

The area $A$ of a triangle is given by the formula:

Substitute the given values:

We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$.

The exact area of $\triangle ABC$ is $\boxed{\frac{15\sqrt{3}}{2}}$.