The other tutor is wrong because he did not interpret correctly.

"Four times a number" is written 4x.

So when 4x is added to 5, we must begin with 5
and add 4x to it, so the correct answer is

5 + 4x

[Notice that it is not "4x + 5", because that would be
when 5 is added to 4x,  It is the same mathematically,
but we must learn to interpret exactly because in other
cases it matters which comes first.] 

Edwin