The expression you've provided defines a binary operation "∘" on the set $M = (5, \infty)$, and the operation is described as:

$x \circ y = xy - 5x - 5y + 30$

where $x$ and $y$ are elements of the set $M$.

Would you like a more detailed explanation on how to approach specific properties of this operation (e.g., associativity, commutativity), or would you like to analyze this operation further in some way?

Here are some questions we could explore:

1. What is the identity element for the operation $\circ$ within $M$?
2. Is the operation $\circ$ commutative (i.e., is $x \circ y = y \circ x$ for all $x, y \in M$)?
3. Is the operation $\circ$ associative (i.e., is $x \circ (y \circ z) = (x \circ y) \circ z$)?
4. Can we define an inverse element for each $x \in M$ such that $x \circ e = e \circ x = x$?
5. How would the operation behave on the boundary value, such as $x = 5$?

Tip: Understanding whether the operation $\circ$ is associative and has an identity element can help determine if it forms a group under this operation.