Is there a divisibility rule of 5?

1+2+3+4+5=151 + 2 + 3 + 4 + 5 = 15 is divisible by 5.
7+8+9+10+11=457 + 8 + 9 + 10 + 11 = 45 is divisible by 5.
23+24+25+26+27=12523 + 24 + 25 + 26 + 27 = 125 is divisible by 5.

Is it true that the sum of any 5 consecutive integers is divisible by 5?

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