  We derive and study distorted, five-dimensional, electrically charged,
non-extremal black holes on the example of a static and "axisymmetric" black
hole distorted by external, electrically neutral matter.The solution satisfies
Einstein-Maxwell equations which admits an $\mathbb{R}^1\times U(1)\times U(1)$
isometry group. The inner horizon remains regular if the distortion fields are
finite and smooth at the outer horizon. There exists a certain duality
transformation between the inner and the outer horizon surfaces which links
surface gravity, electrostatic potential, and space-time curvature invariants
calculated at the black hole horizons. The product of the inner and outer
horizon areas depends only on the black hole's electric charge and the
geometric mean of the areas is the upper (lower) limit for the inner (outer)
horizon area. The horizon areas, electrostatic potential, and surface gravity
satisfy the Smarr formula. We formulated the zeroth and the first laws of
mechanics and thermodynamics of the distorted black hole and found a
correspondence between the global and local forms of the first law. To
illustrate the effect of distortion we consider the dipole-monopole and
quadrupole-quadrupole distortion fields. The relative change in the Kretschamnn
scalar due to the distortion is greater at the outer horizon than at the inner
one. Calculating the maximal proper time of free fall from the outer to the
inner horizons we show that the distortion can noticeably change the black hole
interior. The change depends on type and strength of distortion fields. In
particular, due to the types of distortion fields considered here the black
hole horizons can either come arbitrarily close to or move far from each other.
