Re-Calc from new cell if so many cells are blank

I have 2 columns.

Column E has the amount of time each day.
Column G is where I want the Sum to be displayed.

I need Column G to do a =Sum(E4:E33), but if anywhere in between E4 and E33 there is a period of 5 days where it totals 0 then I want column G to re-add from the first day where there is a amount in it.

Ex: E4 to E10 totals 7 (1 per day), from E11 to E15 totals 0, from E16 to E33 totals 18 (1 per day again).

In Column G at G10 it should total 7, at G11 it should be 6, G12 5 etc until it hits G15 where it sees the 5 previous days nothing was entered so it enters a value of 0, because G15 is set to 0, G16 will start adding from E16 till E33, until somewhere down the line it sees another period of 5 days where it adds up to 0 again.