5 3/4 + 1 5/8

Let's calculate the sum. First, convert the mixed numbers to improper fractions:
$$5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$$
$$1 \frac{5}{8} = \frac{1 \times 8 + 5}{8} = \frac{8 + 5}{8} = \frac{13}{8}$$
Now add the fractions. To do this, we need a common denominator, which is 8:
$$\frac{23}{4} + \frac{13}{8} = \frac{23 \times 2}{4 \times 2} + \frac{13}{8} = \frac{46}{8} + \frac{13}{8} = \frac{46 + 13}{8} = \frac{59}{8}$$
Convert the improper fraction back to a mixed number:
$$\frac{59}{8} = 7 \frac{3}{8}$$
Answer: 7 3/8