Try this
Public Sub FormatOutput()
Dim lastrow As Long
Application.ScreenUpdating = False
lastrow = Worksheets("Prüfliste").Range("A" & Rows.Count).End(xlUp).Row
With Worksheets("Ausgabe")
.Range("A2").Resize(lastrow - 1).FormulaR1C1 = "=Prüfliste!RC"
.Range("B2").Resize(lastrow - 1).Value = Format(Now, "DD.MM.YYYY HH:MM")
.Range("C2").Resize(lastrow - 1).Value = "bydo@vba.ms"
.Range("D2").Resize(lastrow - 1).Value = "bydo"
.Range("E2").Resize(lastrow - 1).FormulaR1C1 = _
"=IF(ISNA(MATCH(Prüfliste!RC[-3],Inventar!C[-2],0)),MATCH(Prüfliste!RC[-3],Inventar!C[-1],0),MATCH(Prüfliste!RC[-3],Inventar!C[-2],0))"
.Range("F2").Resize(lastrow - 1).FormulaR1C1 = _
"=IF(ISNA(RC5),""nicht gefunden"",IF(OR(INDEX(Inventar!C6,RC5)=""aktiv"",INDEX(Inventar!C6,RC5)=""wartend""),"""",INDEX(Inventar!C[-4],RC5)))"
.Range("G2").Resize(lastrow - 1).FormulaR1C1 = _
"=IF(ISNA(RC5),""nicht gefunden"",IF(OR(INDEX(Inventar!C6,RC5)=""aktiv"",INDEX(Inventar!C6,RC5)=""wartend""),"""",INDEX(Inventar!C[-2],RC5)))"
.Range("H2").Resize(lastrow - 1).FormulaR1C1 = _
"=IF(ISNA(RC5),""nicht gefunden"",IF(OR(INDEX(Inventar!C6,RC5)=""aktiv"",INDEX(Inventar!C6,RC5)=""wartend""),"""",INDEX(Inventar!C[-2],RC5)))"
With .Range("A2").Resize(lastrow - 1, 8)
.Value = .Value
End With
.Columns("E:E").Delete
End With
Application.ScreenUpdating = True
End Sub