As long as you remember to enter this with Ctrl+Shift+Enter, there are many ways it would/should work:
=SUMPRODUCT((TRANSPOSE(D2:F2))*(C5:C7)) ... my norm, for clarity, grouped and using the array "and" function (*)
=SUMPRODUCT(TRANSPOSE(D2:F2)*C5:C7) ... same as above, but ungrouped
=SUMPRODUCT(TRANSPOSE(D2:F2),C5:C7) ... same as above, but using a comma