Countifs: Multiple Criteria in Same Range with Other Criteria

Is there a way to count multiple criteria in the same range in a countifs function even though there are other criteria that needs to be considered.

Below is what I came up with but I need to add Math1, Science1, History1, and English2 [edited as first sample was too easy to solve/sample excel file will have other subjects in it. Sorry ] in the 5th criteria. (Note: Not the actual data as it is confidential but is very similar.)


=COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English1",Raw!E:E,"Teacher A")


Basically, I need it to count all English1, English2, English3, English4, and English5 in the same column but still consider all the other variables in the existing formula.

I was thinking nested formula but I can't figure out what function I should use and how to execute it. I also tried this

=COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English1",Raw!E:E,"Teacher A")+COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English2",Raw!E:E,"Teacher A")+COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English3",Raw!E:E,"Teacher A")+COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English4",Raw!E:E,"Teacher A")+COUNTIFS(Raw!A:A,"Jul",Raw!F:F,"Yes",Raw!B:B,"No",Raw!C:C,"Teacher",Raw!D:D,"English5",Raw!E:E,"Teacher A")

but this is too long and would take a lot of time since my data contains numerous teachers, subjects and numerous raw data file entry. Can someone help me with this?