2nd order transfer function
\$G(s)\$ is second order. The denominator polynomial has degree 2 (and is not cancelled by a factor of the numerator polynomial).
The natural frequency and damping ratio can be defined in terms of the roots of the denominator polynomial. The presence of the numerator doesn't affect its calculation. So \$\omega_n^2 = 25\$ and \$2\cdot \zeta \cdot \omega_n = 5\$.
One thing to remember is that the numerator in a transfer function \$\frac{N(s)}{D(s)} = \frac{Y(s)}{X(s)}\$ multiplies to the input \$X(s)\$. The transfer function is defined for a system with zero initial conditions. But, for the same system starting from non-zero initial conditions, the dynamics of the system is still governed by the denominator polynomial of \$G(s)\$. So the natural frequency and damping ratio calculated from the denominator polynomial still hold good (again, assuming that the numerator and denominator do not contain common factors which can be cancelled out).