I've got a 5-dimensional continuous dynamical system, i.e.,
$$ \dot{x}(t)=f(x,y,z,u,w)\\ \dot{y}(t)=g(x,y,z,u,w)\\ \dot{z}(t)=h(x,y,z,u,w)\\ \dot{u}(t)=q(x,y,z,u,w)\\ \dot{w}(t)=p(x,y,z,u,w) $$
Is there a systematic way of writing this system as a Hamiltonian system, without necessarily finding a conserved quantity dependent on all variables? That method has proved itself to be quite difficult.
Thanks in advance.