To solve this equation, we will first simplify the expression on the left side:

2/3 - 1/3(x - 3/2) - 1/2(2x + 1) = 5

First, let's distribute the -1/3 and -1/2:

2/3 - 1/3 * x + 1/3 * 3/2 - 1/2 * 2x - 1/2 * 1 = 5

Simplifying further:

2/3 - 1/3x + 1/2 - x - 1/2 = 5

Now, let's combine like terms:

-1/3x - x + 2/3 - 1/2 + 1/2 = 5

-4/3x + 2/3 = 5

Next, let's get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD), which is 6:

6 * (-4/3x + 2/3) = 6 * 5

-8x + 4 = 30

Now, let's isolate the variable by subtracting 4 from both sides:

-8x = 30 - 4

-8x = 26

Finally, divide both sides by -8 to solve for x:

x = 26 / -8

Simplifying the fraction:

x = -13/4

Therefore, the solution to the equation is x = -13/4.