If $m\ne n=m^2-mn+n^2$ and $m?n=(m+n{)}^2-mn$, then what is the evaluated product value of $(2?3)\times (5\ne 3)$?

Let's break down the solution into separate operations:
Step 1: Evaluate the first term $(2?3)$ using $m?n=(m+n{)}^2-mn$:

$$2?3=(2+3{)}^2-(2\times 3)$$

$$2?3=5^2-6=25-6=19$$

Step 2: Evaluate the second term $(5\ne 3)$ using $m\ne n=m^2-mn+n^2$:

$$5\ne 3=5^2-(5\times 3)+3^2$$

$$5\ne 3=25-15+9=19$$

Step 3: Calculate the product of both values:

$$\text{Product}=19\times 19=361$$