If the mean and the standard deviation of the data

Mean $=5$

$\frac{3+5+7+a+b}{5}=5$

$a+b=10$.....(i)

S.d. $=2 \Rightarrow \sqrt{\frac{\sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}}{5}}=2$

$(3-5)^{2}+(5-5)^{2}+(7-5)^{2}+(a-5)^{2}+(b-5)^{2}=20$

$\Rightarrow 4+0+4+(a-5)^{2}+(b-5)^{2}=20$

$a^{2}+b^{2}-10(a+b)+50=12$

$(a+b)^{2}-2 a b-100+50=12$

$a b=19$    ..........(ii)

Equation is $x^{2}-10 x+19=0$