Hamiltonians associated with the third and fifth Painlevé equations

We obtain a Painlevé-type differential equation for the simplest rational Hamiltonian associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We prove the existence of Hamiltonians of a nonrational type associated with the fifth Painlevé equation in the case $\gamma\ne0$, $\delta=0$. We obtain a generalization of the Garnier and Okamoto formulas for rational Hamiltonians associated with the third Painlevé equation.