-96:(5 2/5-3 12/13)

To solve the expression \(-96:(5 \frac{2}{5} - 3 \frac{12}{13})\), we first need to tackle the operation inside the parentheses.

1. Convert the mixed numbers to improper fractions:

   • For \(5 \frac{2}{5}\): \[ 5 \frac{2}{5} = 5 + \frac{2}{5} = \frac{25}{5} + \frac{2}{5} = \frac{27}{5} \]
   • For \(3 \frac{12}{13}\): \[ 3 \frac{12}{13} = 3 + \frac{12}{13} = \frac{39}{13} + \frac{12}{13} = \frac{51}{13} \]

2. Now substitute these back into the expression: \[ 5 \frac{2}{5} - 3 \frac{12}{13} = \frac{27}{5} - \frac{51}{13} \]

3. To subtract these fractions, we need a common denominator. The least common multiple of \(5\) and \(13\) is \(65\).

   • Convert \(\frac{27}{5}\) to have a denominator of \(65\): \[ \frac{27}{5} = \frac{27 \times 13}{5 \times 13} = \frac{351}{65} \]
   • Convert \(\frac{51}{13}\) to have a denominator of \(65\): \[ \frac{51}{13} = \frac{51 \times 5}{13 \times 5} = \frac{255}{65} \]

4. Now subtract the two fractions: \[ \frac{351}{65} - \frac{255}{65} = \frac{351 - 255}{65} = \frac{96}{65} \]

5. Now substitute this result back into the expression for \(-96\): \[ -96 : \left(\frac{96}{65}\right) \]

6. Division by a fraction is the same as multiplying by its reciprocal: \[ -96 \div \frac{96}{65} = -96 \times \frac{65}{96} \]

7. The \(96\) in the numerator and denominator cancel out: \[ -1 \times 65 = -65 \]

So, the final answer is: \[ \boxed{-65} \]