Subtract 7 rac18 from 5 rac45.

To convert a mixed number $a\frac{b}{c}$ to an improper fraction, use the formula $\frac{(a \times c) + b}{c}$.

For $7\frac{1}{8}$:

$$7\frac{1}{8} = \frac{(7 \times 8) + 1}{8} = \frac{56 + 1}{8} = \frac{57}{8}$$

For $5\frac{4}{5}$:

$$5\frac{4}{5} = \frac{(5 \times 5) + 4}{5} = \frac{25 + 4}{5} = \frac{29}{5}$$

The denominators are 8 and 5. The least common multiple (LCM) of 8 and 5 is $8 \times 5 = 40$.

Convert $\frac{57}{8}$ to an equivalent fraction with a denominator of 40:

$$\frac{57}{8} = \frac{57 \times 5}{8 \times 5} = \frac{285}{40}$$

Convert $\frac{29}{5}$ to an equivalent fraction with a denominator of 40:

$$\frac{29}{5} = \frac{29 \times 8}{5 \times 8} = \frac{232}{40}$$

Now subtract the fractions with the common denominator:

$$\frac{285}{40} - \frac{232}{40} = \frac{285 - 232}{40} = \frac{53}{40}$$

Divide the numerator (53) by the denominator (40).
$53 \div 40 = 1$ with a remainder of $53 - (1 \times 40) = 13$.
The quotient (1) is the whole number part, and the remainder (13) is the new numerator over the original denominator (40).

$$\frac{53}{40} = 1\frac{13}{40}$$

The final answer is $1\frac{13}{40}$.