авторI have the following problem:

In cells A1:E1: 1, 2, 3, 4, 5
In cells A2:E2: 6, 7, 8, 9, 10

In cells A5:E5: 21, 22, 23, 24, 25

Now I want to total diagonally (A1, B2, C3, D4 and E5) and I do that by
the formula:
=SUM((ROW(A1:A5)=COLUMN(A1:E1))*(A1:E5)) - array entered.

This works fine (sum =65), but I wondered how can I total diagonally "the
other way" (here A5, B4, C3, D2 and E1)?

To sum A5:E1 diagonally, use:

=SUM(N(OFFSET(E1,ROW(1:5)-1,-1*ROW(1:5)+1)))

Or (not Array Entered):
=SUMPRODUCT(N(OFFSET(E1,ROW(INDIRECT("1:5"))-1,-1*ROW(INDIRECT("1:5"))+1)))

It would be better to use ROW(INDIRECT("1:5") in all the formulas, like

=SUM(N(OFFSET(E1,ROW(INDIRECT("1:5"))-1,-1*ROW(INDIRECT("1:5"))+1)))

as inserting a row above row 5 will change the reference.

To sum across sheets (Sheet1!A1 Sheet2!B2 Sheet3!C3..etc) use:

=SUM(N(INDIRECT("Sheet"&ROW(1:5)&"!"&ADDRESS(ROW(1:5),ROW(1:5)))))

Or (not Array Entered):

=SUMPRODUCT(N(INDIRECT("Sheet"&ROW(1:5)&"!"&ADDRESS(ROW(1:5),ROW(1:5)))))