Is it possible to combine a SUM Function with an IF
statement that will allow me to add multiple cells, but
leave the cell blank if the answer is zero?

Here's what I tried, but to no avail.
In cell F5, I have the following formula:
=(SUM(C5:E5),IF(F5=0,"",(SUM(C5:E5)))

Is there something wrong with the formula, or is the
combination of functions/statements not allowed? Any
help would be greatly appreciated.

Sincerely,
Josh