Instead of deleting just two criteria in the code ("apples" &
"oranges"), I need it to look at values in string on Sheet "grapes",
Reference A5:A15.

Sub Delete_with_Autofilter_Two_Criteria1()
Dim DeleteValue1 As String
Dim DeleteValue2 As String
Dim rng As Range
Dim calcmode As Long

With Application
calcmode = .Calculation
.Calculation = xlCalculationManual
.ScreenUpdating = False
End With

'Fill in the two values that you want to delete
DeleteValue1 = "apples"
DeleteValue2 = "oranges"

'Sheet with the data, you can also use Sheets("MySheet")
With ActiveSheet

'Firstly, remove the AutoFilter
.AutoFilterMode = False

'Apply the filter
.Range("H1:H" & .Rows.Count).AutoFilter Field:=1, _
Criteria1:=DeleteValue1, Operator:=xlOr,
Criteria2:=DeleteValue2

With .AutoFilter.Range
On Error Resume Next
Set rng = .Offset(1, 0).Resize(.Rows.Count - 1, 1) _
.SpecialCells(xlCellTypeVisible)
On Error GoTo 0
If Not rng Is Nothing Then rng.EntireRow.Delete
End With

'Remove the AutoFilter
.AutoFilterMode = False
End With

With Application
.ScreenUpdating = True
.Calculation = calcmode
End With

End Sub