Evaluate the expression: 3/4 of 5 1/3 + 6 2/5 divided by 1 1/5 - 1 1/5

$$5\frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3}$$ $$6\frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{32}{5}$$ $$1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$$ $$1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}$$

The expression becomes:

$$\frac{3}{4} \text{ of } \frac{16}{3} + \frac{32}{5} \div \frac{4}{3} - \frac{6}{5}$$

$$\frac{3}{4} \times \frac{16}{3} = \frac{3 \times 16}{4 \times 3} = \frac{48}{12} = 4$$

The expression is now:

$$4 + \frac{32}{5} \div \frac{4}{3} - \frac{6}{5}$$

$$\frac{32}{5} \div \frac{4}{3} = \frac{32}{5} \times \frac{3}{4} = \frac{32 \times 3}{5 \times 4} = \frac{96}{20}$$

Simplify the fraction:

$$\frac{96}{20} = \frac{24}{5}$$

The expression is now:

$$4 + \frac{24}{5} - \frac{6}{5}$$

First, add $4 + \frac{24}{5}$. Convert 4 to a fraction with a denominator of 5:

$$4 = \frac{4 \times 5}{5} = \frac{20}{5}$$ $$\frac{20}{5} + \frac{24}{5} = \frac{20+24}{5} = \frac{44}{5}$$

Now, subtract $\frac{6}{5}$:

$$\frac{44}{5} - \frac{6}{5} = \frac{44-6}{5} = \frac{38}{5}$$

The answer can also be expressed as a mixed number:

$$\frac{38}{5} = 7\frac{3}{5}$$

The value of the expression is $\boxed{\frac{38}{5}}$ or $\boxed{7\frac{3}{5}}$.