  We study general classes and properties of extremal and non-extremal static
black-hole solutions of N=2, d=5 supergravity coupled to vector multiplets
using the recently proposed H-FGK formalism, which we also extend to static
black strings. We explain how to determine the integration constants and
physical parameters of the black-hole and black-string solutions. We derive
some model-independent statements, including the transformation of non-extremal
flow equations to the form of those for the extremal flow. We apply our methods
to the construction of example solutions (among others a new extremal string
solution of heterotic string theory on K_3 \times S^1). In the cases where we
have calculated it explicitly, the product of areas of the inner and outer
horizon of a non-extremal solution coincides with the square of the
moduli-independent area of the horizon of the extremal solution with the same
charges.
