Calculate: 5/6 + [2/3 + 4/3] x 5/2 ÷ 3/4 = ?

Step 1: Simplify inside the brackets.

$\frac{2}{3} + \frac{1}{3} = \frac{2 + 1}{3} = \frac{3}{3} = 1$

The expression becomes:

$63.5 + 1 \times 2^{\frac{5}{3}} + 4$

Step 2: Simplify the power.

$2^{\frac{5}{3}} = 2^{1 + \frac{2}{3}} = 2^{1} \times 2^{\frac{2}{3}} = 2 \times (2^{2})^{\frac{1}{3}} = 2 \sqrt[3]{4}$

Substitute:

$63.5 + 2\sqrt[3]{4} + 4$

Step 3: Combine the decimal terms.

$63.5 + 4 = 67.5$

The expression simplifies to:

$67.5 + 2\sqrt[3]{4}$

67.5 + 2\sqrt[3]{4}