ClearAll[f]
f = Transpose @ Delete[Position[#[[5]], 0]] @ Transpose @ # &;
Example:
SeedRandom[1234]
table = RandomInteger[5, {9, 10}];
MatrixForm[table]
MatrixForm[MapAt[Style[#, Blue] &, #, {5, All}] /.
Style[0, _] :> Style[0, Red, Bold]] & @ table
table2 = f@table;f @ table;
MatrixForm[table2]
Also
ClearAll[f2]
f2 = #[[All, Complement[Range@Length@#, Flatten@Position[#, 0]] &@#[[5]]]] &;
f2 @ table == f @ table
True