Let's solve the expression step by step.

The expression is:

\[
\left( \frac{6 - \frac{2}{3} + \frac{1}{2}}{3} \right) - \left( 5 + \frac{5}{3} - \frac{3}{2} \right) - \left( \frac{3 - \frac{7}{3} + \frac{5}{2}}{3} \right)
\]

### Step 1: Simplify each part

1. **First part:**
- \( 6 - \frac{2}{3} + \frac{1}{2} \)
- First, find a common denominator (6):
\[
6 = \frac{36}{6}, \quad \frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}
\]
- So,
\[
6 - \frac{2}{3} + \frac{1}{2} = \frac{36 - 4 + 3}{6} = \frac{35}{6}
\]
- Now, divide by 3:
\[
\frac{35/6}{3} = \frac{35}{18}
\]

2. **Second part:**
- \( 5 + \frac{5}{3} - \frac{3}{2} \)
- Find a common denominator (6):
\[
5 = \frac{30}{6}, \quad \frac{5}{3} = \frac{10}{6}, \quad \frac{3}{2} = \frac{9}{6}
\]
- So,
\[
5 + \frac{5}{3} - \frac{3}{2} = \frac{30 + 10 - 9}{6} = \frac{31}{6}
\]

3. **Third part:**
- \( \frac{3 - \frac{7}{3} + \frac{5}{2}}{3} \)
- First, simplify the numerator \( 3 - \frac{7}{3} + \frac{5}{2} \).
- Find a common denominator (6):
\[
3 = \frac{18}{6}, \quad \frac{7}{3} = \frac{14}{6}, \quad \frac{5}{2} = \frac{15}{6}
\]
- So,
\[
3 - \frac{7}{3} + \frac{5}{2} = \frac{18 - 14 + 15}{6} = \frac{19}{6}
\]
- Now, divide by 3:
\[
\frac{19/6}{3} = \frac{19}{18}
\]

### Step 2: Combine the parts
Now we have:
\[
\frac{35}{18} - \frac{31}{6} - \frac{19}{18}
\]

Convert \(\frac{31}{6}\) to a fraction with a denominator of 18:
\[
\frac{31}{6} = \frac{93}{18}
\]

Now substitute:
\[
\frac{35}{18} - \frac{93}{18} - \frac{19}{18} = \frac{35 - 93 - 19}{18} = \frac{-77}{18}
\]

### Final Answer:
\[
\frac{-77}{18}
\]