This question is an application of the factoring of the difference of two squares.

A^2 - b^2 = (a + b)(a - b)

You have

a = √10

b = √5

The square of a square root is the number itself.

A^2 = (√10)^2 = 10

b^2 = (√5)^2 = 5

((√10) + (√5))((√10 - (√5))

= (√10)^2 - (√5)^2

= 10 - 5

It is a good idea to memorize this factoring. It shows up a lot in algebra problems. It can actually be usefully applied to compute values in your head that might otherwise be difficult to do. This problem is an example of that.

A^2 - b^2 = (a + b)(a - b)

You have

a = √10

b = √5

The square of a square root is the number itself.

A^2 = (√10)^2 = 10

b^2 = (√5)^2 = 5

((√10) + (√5))((√10 - (√5))

= (√10)^2 - (√5)^2

= 10 - 5

**= 5**It is a good idea to memorize this factoring. It shows up a lot in algebra problems. It can actually be usefully applied to compute values in your head that might otherwise be difficult to do. This problem is an example of that.