To find the sine of an angle \( \theta \) that has a cosine value of \( \cos \theta = \frac{2}{5} \) and lies in Quadrant IV, we can use the Pythagorean identity:
\[ \sin^2 \theta + \cos^2 \theta = 1. \]
First, we know \( \cos \theta = \frac{2}{5} \). We can substitute this value into the Pythagorean identity. Calculating \( \cos^2 \theta \):
\[ \cos^2 \theta = \left(\frac{2}{5}\right)^2 = \frac{4}{25}. \]
Substituting this into the Pythagorean identity gives:
\[ \sin^2 \theta + \frac{4}{25} = 1. \]
Next, we can isolate \( \sin^2 \theta \):
\[ \sin^2 \theta = 1 - \frac{4}{25}. \]
To perform the subtraction, we convert \( 1 \) into a fraction with the same denominator:
\[ 1 = \frac{25}{25}, \]
so we have:
\[ \sin^2 \theta = \frac{25}{25} - \frac{4}{25} = \frac{21}{25}. \]
Now, take the square root of both sides:
\[ \sin \theta = \pm \sqrt{\frac{21}{25}}. \]
This simplifies to:
\[ \sin \theta = \pm \frac{\sqrt{21}}{5}. \]
Since the angle \( \theta \) is in Quadrant IV and the sine function is negative in this quadrant, we take the negative root:
\[ \sin \theta = -\frac{\sqrt{21}}{5}. \]
Thus, the sine of the angle is:
\[ \boxed{-\frac{\sqrt{21}}{5}}. \]