How do I get the count of non matching cells in a row between two sheets?

I have two sheets, Sheet A containing a truth table like such:

    A B C D E
Foo T F F T F
Bar T F F F F

Sheet B contains another table:

A B C D E
T F F T F

I need to add a column to table A counting how many cells match the corresponding cell in sheet B, as such:

Foo T F F T F 2
Bar T F F F F 1

Best I could come up with for the first count cell was

=COUNTIF(B1:F1,B1:F1=INDIRECT("sheet-b!A2:E2"))

but this gives me 0 even though it should be 2.