5⅓*2¼:⅘

To solve the expression 5⅓ * 2¼ : ⅘, we need to follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

First, let's convert the mixed numbers to improper fractions: 5⅓ = 5 + 1/3 = 15/3 + 1/3 = 16/3 2¼ = 2 + 1/4 = 8/4 + 1/4 = 9/4

Now, let's perform the multiplication: 16/3 * 9/4 = (16 * 9) / (3 * 4) = 144/12 = 12

Finally, let's perform the division: 12 : ⅘ = 12 * 5/4 = (12 * 5) / 4 = 60/4 = 15

Therefore, the solution is 15.