'Check reference column and select the same number of rows in start and end columns
Sub selectByUsedRows(usedCol As String, selectStartCol As String, selectEndCol As String)
n = Range(usedCol & "1").End(xlDown).Row
Range(selectStartCol & "1:" & selectEndCol & n).Select
End Sub

'Dynamically select columns A to C with as many rows as are in A
Sub test()
refCol = "A"
selectStartCol = "A"
selectEndCol = "C"
selectByUsedRows refCol, selectStartCol, selectEndCol

'Code works until this point. There is now an active selection of A1:C8. 
'The following is hypothetical

Dim rngSelection As Range
Set rngSelection = ActiveSelection
Range(rngSourceData).CurrentRegion.Name = "rngSourceData"

Set objTable = Sheet5.PivotTableWizard

ActiveWorkbook.PivotCaches.Create(SourceType:=xlDatabase, SourceData:= _
    rngSourceData, Version:=xlPivotTableVersion14).CreatePivotTable _
    TableDestination:="Sheet5!R1C4", TableName:="PivotTable1", DefaultVersion _
    :=xlPivotTableVersion14
End Sub