In this paper, we study distorted, five-dimensional, electrically charged (nonextremal) black holes on the example of a static and "axisymmetric" black hole distorted by external, electrically neutral matter. Such a black hole is represented by the solution derived here of the Einstein-Maxwell equations which admits an R-1 x U(1) x U(1) isometry group. The external matter, which is "located" at the asymptotic infinity, is not included in the solution. The space-time singularities are located behind the black hole's inner (Cauchy) horizon, provided that the sources of the distortion satisfy the strong energy condition. The inner (Cauchy) horizon remains regular if the distortion fields are finite and smooth at the outer horizon. The solution has some remarkable properties. 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 electromagnetic field invariant calculated at the horizons is proportional to the squared surface gravity of the horizons. 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 Kretschmann scalar due to the distortion is greater at the outer horizon than at the inner one. By 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 the 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.
