To solve the expression \((-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7})\), we can simplify it step by step.
- Convert the division into multiplication by taking the reciprocal of the divisor:
\[ (-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times \left(-\frac{16}{3}\right) \times (-\frac{5}{7}) \]
- Now, we can combine all the fractions:
\[ = \frac{-3 \times 5 \times 7 \times -16 \times -5}{5 \times 16 \times 12 \times -3 \times 7} \]
- Let's simplify step by step:
- The numerator is \(-3 \times 5 \times 7 \times -16 \times -5\).
- The denominator is \(5 \times 16 \times 12 \times -3 \times 7\).
- We can start canceling terms from the numerator and denominator:
- The \(-3\) in the numerator and denominator cancels out.
- The \(5\) in the numerator and denominator cancels out.
- The \(7\) in the numerator and denominator cancels out.
After canceling, we simplify:
\[ = \frac{(-16) \times (-5)}{16 \times 12} \]
- This simplifies to:
\[ = \frac{80}{192} \]
- Now we simplify \(\frac{80}{192}\):
The greatest common divisor of 80 and 192 is 16.
Dividing the numerator and the denominator by 16 gives us:
\[ = \frac{5}{12} \]
Thus, the final answer is:
\[ \boxed{\frac{5}{12}} \]