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Default Averaging every 5th cell while omitting zeros

Greetings! Thank you for your interest in my question, I have been bashing my
head in trying to figure it out. In a column, I want to add every FIFTH cell
starting with row 7 and ending with row 272. Meanwhile, I need to exclude all
the cells with zero so the averaging only divides by the number of cells with
a numeral. I have tried entering each 5th row individually in various
formulas and I have tried defining a name and using that in the formulas but
nothing has worked, I keep getting an error each time. I would really
appreciate any help! Thank you.
 
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