You are not far off.

Try something like

Sub moveit()
'
' moveit Macro
'
Dim Move2Cat As String
    Move2Cat = Range("A5").Value
    Range("AA15:AW15").Copy
    Select Case Move2Cat
        Case Is = "Resisdental"
            Worksheets("Res.Contractors").Activate
        Case Is = "Commerical"
            Worksheets("Res.Contractors").Activate
        '..... add others here
    
    
    End Select
    Range("B" & Rows.Count).End(xlUp).Offset(1, 0).PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
        :=False, Transpose:=False
    Sheets("Data Entry").Activate
    Range("C4:C26").ClearContents
    Range("C4").Select
    
End Sub