He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.
He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.
