In Poisson distribution :
Mean = Variance as n is large and p is small
And we know:
$\text{Variance} = E\left(X^{2}\right) - [ E(X) ]^{2}$
$\Rightarrow E(X^{2}) = [ E(X) ]^{2} + \text{Variance}$
$\Rightarrow E(X^{2}) = 5^{2} + 5$
$\Rightarrow E(X^{2}) = 30$
So, by linearity of expectation,
$E[(X + 2)^{2} ] = E[ X^{2} + 4X + 4 ]$
$\quad = E(X^{2}) + 4 E(X) + 4$
$\quad =30 + (4 \times 5) + 4$
$\quad = 54$