Need to count if the difference in values between two arrays is less than 5

I have three columns, which I have simplified for this problem, but they are team, start and finish. They are located in another workbook, so i cannot generate a fourth column to produce the differences between the start and finish.

I would like to count if the difference between (Finish-Start) is less than 5, and team equals 2.

In my example worksheet (attached), the answer should be 2, but I can only get that by generating the fourth column "difference" first and using "=COUNTIFS(A3:A22, "=2", D3:D22, "<=5")" (cell D23), which I can't do in my original problem, because I can't generate that column in the new workbook, or original workbook.

I have tried "=countifs(A3:A22, "=2", b3:b22-c3:c22, "<=5")" but this doesn't work . . . but that may explain better the logic I am trying to introduce into a cell.

Thank you in advance.

=SUMPRODUCT(--(A3:A22=2),--(C3:C22-B3:B22<=5))

Just normally Enter

Thank you everyone. I am going to try some of these solutions on my larger file and see if they work. I will be sure to let everyone know.

I ended up using tigeravatar and teethless mama's suggestion. Thank you again for your help.