The number of ways each husband can sit to the left of his wife There are 5 husband/wife couples. What is the number of ways we can sit the couples around a circular table with each husband sitting to the left of his wife?

I'm assuming you mean that the husband sits directly to the left of his wife, in which case the number of ways we can sit the couples is simply the number of ways to place five objects around a circle.

This is just $5!$, divided by the number of rotational symmetries, which is $5$, to give $$\frac{5 \cdot 4 \cdot 3 \cdot 2}{5} = \boxed{24}$$

Alternatively, if you mean that the husband can sit anywhere to the left of his wife (not necessarily adjacent to her), then _anywhere_ on the circular table is to the left of _every_ person, so in this case the answer is just the number of ways we can sit $10$ people around a circular table, which is $$\frac{10!}{10}= 9! = 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 = \boxed{362880}$$