  In this paper, the overcharging problem and thermodynamics in the extended
phase spaces of the five-dimensional spherically symmetric topological black
holes are investigated by absorptions of scalar particles and fermions. The
cosmological constant is regarded as a variable related to pressure and its
conjugate quantity is a thermodynamic volume. The first law of thermodynamics
is recovered. The second law is violated in the extended phase space of the
extremal and near-extremal black holes. The overcharging problem is tested by
the existence of the event horizons. The event horizon is determined by the
metric component $f(r)$. The minimal values of the metric component at the
final stage show that the extremal and near-extremal black holes can not be
overcharged.
