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Any even number can be expressed as a multiple of two. If you have 5 even numbers, then we can label them as such:

a1 = 2*b1

a2 = 2*b2

a3 = 2*b3

a4 = 2*b4

a5 = 2*b5

Where bn is an arbitrary integer

So we therefore have:

a1 + a2 + a3 + a4 + a5 = 2*b1 + 2*b2 +2*b3 + 2*b4 + 2*b5

= 2*(b1 + b2 +b3 + b4 + b5)

We can then let b1 + b2 +b3 + b4 + b5 = c

because our sum of 5 numbers is equal to 2*c, this means that the sum is a multiple of 2, and therefore even.

QED.

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