To solve the equation 5/8(x-2) - 2/3(x+2) = -1, we need to first simplify the expression on both sides of the equation.

First, let's distribute the fractions:

5/8 x - 5/4 - 2/3 x - 4/3 = -1

Next, let's combine like terms:

(5/8 - 2/3) * x - 5/4 - 4/3 = -1

To combine the fractions, we need to find a common denominator. The least common denominator between 8 and 3 is 24. So, we'll rewrite the equation:

((15 - 16)/24) * x - (15/4 + 32/12) = -1

((-1/24) * x - (45/12) = -1

Now, combine the fractions again:

-1/24 * x - 45/12 = -1

To solve for x, we'll isolate the variable by moving the constant terms to the other side of the equation:

-1/24 * x = -1 + 45/12

-1/24 * x = -1 + 3.75

-1/24 * x = 2.75

Now, solve for x by multiplying both sides by the reciprocal of -1/24:

x = 2.75 / (-1/24)

x = 2.75 * (-24)

x = -66

Therefore, the solution to the equation 5/8(x-2) - 2/3(x+2) = -1 is x = -66.