To simplify the expression $\frac{a^3b^2}{cd} \times \frac{c}{ab^5}$, we will first multiply the numerators together and the denominators together:

$\frac{a^3b^2 \cdot c}{cd \cdot ab^5}$

We then simplify by canceling out common terms in the numerator and denominator:

1. The $c$ in the numerator and the $c$ in the denominator cancel out.
2. $a^3$ in the numerator and $a$ in the denominator leaves $a^{3-1} = a^2$.
3. $b^2$ in the numerator and $b^5$ in the denominator leaves $b^{2-5} = b^{-3}$, or $\frac{1}{b^3}$.

Thus, the simplified expression is:

$\frac{a^2}{db^3}$

Do you have any further questions on this problem or need more detailed explanations? Here are a few related questions you might consider:

1. How do the laws of exponents work when multiplying and dividing terms?
2. What happens when the same variable appears in both the numerator and the denominator?
3. Could you simplify an expression where variables have negative exponents initially?
4. How would you simplify an expression with more complex variables or higher powers?
5. What are some common mistakes to avoid when simplifying algebraic expressions?

Tip: Always remember to combine like terms and simplify exponents step by step when dealing with algebraic fractions.