What are they talking about in these maths question?

We have an odd number (ie 5) multiplied by

(an even number (2*n) plus an odd number)

An even number plus an odd number is an odd number

So we have the product of two odd numbers.

In general, that's (2*a + 1)*(2*b + 1)

= 4*b^2 + 2*a + 2*b + 1

The first three terms are clearly even

The 1 at the end makes it odd.

In short, the expression you give is always odd.

Always odd.

2n + 3 is always odd

Odd number times 5 is always odd.