To solve the equation \((X + 0.3) + (X + 0.8) + (X + 1.3) + \ldots + (X + 4.3) + (X + 4.8) = 75.5\), we first need to determine the number of terms in the sequence and then solve for \(X\).

The sequence starts at \(X + 0.3\) and ends at \(X + 4.8\). The terms increase by 0.5 each time. Let's list the terms to identify the pattern:

1. \(X + 0.3\)
2. \(X + 0.8\)
3. \(X + 1.3\)
4. \(X + 1.8\)
5. \(X + 2.3\)
6. \(X + 2.8\)
7. \(X + 3.3\)
8. \(X + 3.8\)
9. \(X + 4.3\)
10. \(X + 4.8\)

There are 10 terms in the sequence. We can sum these terms as follows:

\[
\sum_{i=1}^{10} (X + a_i)
\]

where \(a_i\) represents the constant part of each term. The constants are 0.3, 0.8, 1.3, 1.8, 2.3, 2.8, 3.3, 3.8, 4.3, and 4.8.

First, let's sum the constants:

\[
0.3 + 0.8 + 1.3 + 1.8 + 2.3 + 2.8 + 3.3 + 3.8 + 4.3 + 4.8
\]

To simplify the addition, we can pair the terms:

\[
(0.3 + 4.8) + (0.8 + 4.3) + (1.3 + 3.8) + (1.8 + 3.3) + (2.3 + 2.8)
\]

Each pair sums to 5.1:

\[
5.1 + 5.1 + 5.1 + 5.1 + 5.1 = 25.5
\]

Now, we can write the equation for the sum of the sequence:

\[
10X + 25.5 = 75.5
\]

To find \(X\), we solve the equation:

\[
10X + 25.5 = 75.5
\]

Subtract 25.5 from both sides:

\[
10X = 50
\]

Divide by 10:

\[
X = 5
\]

So, the value of \(X\) is \(5\).