We need to evaluate the expression $ -\frac{3}{4} + 1\frac{5}{8} $.

1. Problem Description

We need to evaluate the expression $-\frac{3}{4} + 1\frac{5}{8}$.

2. Solution Steps

First, convert the mixed number $1\frac{5}{8}$ to an improper fraction.

$1\frac{5}{8} = \frac{1*8 + 5}{8} = \frac{8 + 5}{8} = \frac{13}{8}$.

Now, the expression becomes $-\frac{3}{4} + \frac{13}{8}$.

To add the fractions, we need a common denominator. The least common multiple of 4 and 8 is

8. Convert $-\frac{3}{4}$ to an equivalent fraction with a denominator of 8:

$-\frac{3}{4} = -\frac{3 * 2}{4 * 2} = -\frac{6}{8}$.

Now the expression is $-\frac{6}{8} + \frac{13}{8}$.

$-\frac{6}{8} + \frac{13}{8} = \frac{-6 + 13}{8} = \frac{7}{8}$.

3. Final Answer

The final answer is $\frac{7}{8}$.