We will solve the expression \((-3/5) \times (5/16) \times (7/12) \div (-3/16) \times (-5/7)\) step-by-step.
First, we can rewrite the division as multiplication by the reciprocal:
\[ (-3/5) \times (5/16) \times (7/12) \times \frac{-16}{3} \times \frac{-7}{5} \]
Next, let's focus on the multiplication of all the fractions in the expression:
\[ (-3/5) \times (5/16) \times (7/12) \times \frac{-16}{3} \times \frac{-7}{5} \]
Now we can combine the fractions:
\[ = \frac{(-3) \times 5 \times 7 \times (-16) \times (-7)}{5 \times 16 \times 12 \times (-3) \times 5} \]
Now we can simplify the expression:
- Note that the \(-3\) in the numerator and the denominator cancels out.
- The \(5\) in the numerator and denominator cancels out too.
- There are two \(-16\) in the numerator which can be adjusted to have one as positive after the cancellation.
Thus, we have:
\[ = \frac{(7) \times (-16) \times (-7)}{16 \times 12} \]
Now we can simplify \((-16) \times (-7)\):
\[ = 16 \times 7 = 112 \]
So, the expression simplifies to:
\[ = \frac{112}{16 \times 12} \]
Now let's compute \(16 \times 12 = 192\):
So we now have:
\[ = \frac{112}{192} \]
Next, let's simplify \(\frac{112}{192}\) by finding the greatest common divisor (GCD) of 112 and 192, which is 16:
\[ = \frac{112 \div 16}{192 \div 16} = \frac{7}{12} \]
Thus, the final answer is:
\[ \boxed{\frac{7}{12}} \]