Why can't 7x 5 be factored?

I will assume you mean 7x + 5. In general, a binomial (two terms) can ONLY be factored if both terms have a common factor, OR you have a difference of squares. No other cases are possible, since the product of two binomials is, in general, a trinomial (three terms). Since none of these special cases apply, the expression can't be factored.