To solve the equation \( X - \frac{3}{4} + 5 = \frac{25}{2} \), follow these steps:

1. **Combine like terms**:
To simplify, combine the constant terms on the left side.

\[
5 = \frac{10}{2} \quad (\text{convert } 5 \text{ to a fraction with a denominator of } 2)
\]

Thus, the equation becomes:
\[
X - \frac{3}{4} + \frac{10}{2} = \frac{25}{2}
\]

2. **Rewrite**:
Now write it as:
\[
X - \frac{3}{4} + \frac{10}{2} = \frac{25}{2}
\]

Combine \(-\frac{3}{4}\) and \(\frac{10}{2} = \frac{10}{2} = \frac{20}{4}\):
\[
X + \left(\frac{20}{4} - \frac{3}{4}\right) = \frac{25}{2}
\]

Simplifying gives:
\[
X + \frac{17}{4} = \frac{25}{2}
\]

3. **Isolate \(X\)**:
To isolate \(X\), subtract \(\frac{17}{4}\) from both sides:
\[
X = \frac{25}{2} - \frac{17}{4}
\]

Convert \(\frac{25}{2}\) to a fraction with a denominator of 4:
\[
\frac{25}{2} = \frac{50}{4}
\]

Now substitute:
\[
X = \frac{50}{4} - \frac{17}{4}
\]

This simplifies to:
\[
X = \frac{33}{4}
\]

Thus, the solution is:
\[
X = \frac{33}{4}
\] or \(8.25\) in decimal form.