Ashu is x years old while his mother Mrs Veena is x2 years old

Given that Ashu's present age is $=x$ years and his mother Mrs. Veena is $=x^{2}$ years

Then according to question,

Five years later, Ashu's is $=(x+5)$ years

And his mother Mrs. Veena is $=\left(x^{2}+5\right)$ years

Thus

$x^{2}+5=3(x+5)$

$x^{2}+5=3 x+15$

$x^{2}+5-3 x-15=0$

$x^{2}-3 x+10=0$

$x^{2}-5 x+2 x+10=0$

$x(x-5)+2(x-5)=0$

$(x-5)(x+2)=0$

So, either 

$(x-5)=0$

$x=5$

Or

$(x+2)=0$

$x=-2$

But, the age can never be negative.

Therefore, when $x=5$ then

$x^{2}=5^{2}$

$=25$

Hence, Ashu's present age is $=5$ years and his mother Mrs. Veena is $=25$ years