Simplify the Expression: 13x + 5 - 4.5x + 7.5x

To solve this problem, we'll follow these steps:

• Step 1: Identify and combine like terms involving $x$.
• Step 2: Maintain any constant terms separately.

Now, let's work through each step:
Step 1: The expression to simplify is $13x + 5 - 4.5x + 7.5x$.
Combine the coefficients of $x$: $13 + 7.5 - 4.5$.
Carrying out this calculation: $13 + 7.5 - 4.5 = 16$.

Step 2: The constant term is $5$, which remains unchanged.

Therefore, the simplified expression is $16x + 5$.

The correct choice for this expression is choice 1: $16x + 5$.