To solve the equation \( X + \frac{1}{2} = -\frac{3}{2} - \frac{1}{5} \), we can follow these steps:

1. First, simplify the right side of the equation. To do this, we need a common denominator for \(-\frac{3}{2}\) and \(-\frac{1}{5}\). The common denominator between 2 and 5 is 10.

\[
-\frac{3}{2} = -\frac{3 \cdot 5}{2 \cdot 5} = -\frac{15}{10}
\]
\[
-\frac{1}{5} = -\frac{1 \cdot 2}{5 \cdot 2} = -\frac{2}{10}
\]

2. Now, combine the fractions on the right-hand side:

\[
-\frac{15}{10} - \frac{2}{10} = -\frac{15 + 2}{10} = -\frac{17}{10}
\]

3. Now, substitute back into the equation:

\[
X + \frac{1}{2} = -\frac{17}{10}
\]

4. Next, we isolate \( X \) by subtracting \( \frac{1}{2} \) from both sides:

\[
X = -\frac{17}{10} - \frac{1}{2}
\]

5. Convert \( \frac{1}{2} \) into a fraction with a denominator of 10:

\[
\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}
\]

6. Now substitute this back into the equation:

\[
X = -\frac{17}{10} - \frac{5}{10} = -\frac{17 + 5}{10} = -\frac{22}{10}
\]

7. Finally, simplify the fraction:

\[
X = -\frac{22}{10} = -\frac{11}{5}
\]

So, the solution is

\[
\boxed{-\frac{11}{5}}
\]