=SUMPRODUCT(--(A1:A233>=1),--(A1:A233<=5))
or
=SUM(COUNTIF(A1:A233,{1,2,3,4,5}))

You need a UDF to return an array of TRUE/FALSE for formulae

Function IsFormula(rng As Range)
Dim cell As Range, row As Range
Dim i As Long, j As Long
Dim aryFormulae As Variant

   If rng.Areas.Count > 1 Then
       IsFormula = CVErr(xlErrValue)
       Exit Function
   End If

   If rng.Cells.Count = 1 Then

       ReDim aryFormulae(1 To 1)
       aryFormulae(1) = rng.HasFormula
   Else

       aryFormulae = rng.Value
       i = 0

       For Each row In rng.Rows
           i = i + 1
           j = 0

           For Each cell In row.Cells
               j = j + 1
               aryFormulae(i, j) = cell.HasFormula
           Next cell
       Next row
   End If

   IsFormula = aryFormulae
End Function

and then count them like so

=SUMPRODUCT(--(IsFormula(A1:A10)))