To solve this equation, we need to simplify both sides and isolate the variable x.

Starting with the left side of the equation:
x - 1/4

To simplify this, we need to find a common denominator for 1 and 4, which is 4. So we can rewrite 1 as 4/4:
x - 4/4 = 5/8 * 2/3

Simplifying further:
x - 1/4 = 10/24

Now, let's simplify the right side of the equation:
5/8 * 2/3

To multiply fractions, we multiply the numerators together and the denominators together:
(5 * 2) / (8 * 3) = 10/24

So the equation becomes:
x - 1/4 = 10/24

To isolate x, we need to get rid of the -1/4 on the left side. We can do this by adding 1/4 to both sides of the equation:
x - 1/4 + 1/4 = 10/24 + 1/4

Simplifying:
x = 10/24 + 6/24

Combining the fractions:
x = 16/24

Simplifying further, we can divide both the numerator and denominator by their greatest common divisor, which is 8:
x = 2/3

So the solution to the equation is x = 2/3.