Noted some typos and a little cleanup:

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Option Explicit
Sub AvgGT15()
Dim AOI As Range
Dim StoreResult As Range
Dim c As Range
Dim i As Long
Dim Result()

Set StoreResult = [M1]
Set AOI = [D1:D5000]
[M1:M5000].ClearContents

i = 0
ReDim Preserve Result(i)

For Each c In AOI
If c.Value < 15 Then
If Result(0) = 15 Then
StoreResult.Value = Application.WorksheetFunction.Average(Result())
Set StoreResult = StoreResult.Offset(1, 0)
End If
i = 0
Result(0) = 0
Else
ReDim Preserve Result(i)
Result(i) = c.Value
i = i + 1
End If
Next c

If Result(0) = 15 Then StoreResult.Value = _
Application.WorksheetFunction.Average(Result())

End Sub
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--ron