  We apply Kaluza's procedure to Eddington-inspired Born-Infeld action in
gravity in five dimensions. The resulting action contains, in addition to the
usual four-dimensional actions for gravity and electromagnetism, nonlinear
couplings between the electromagnetic field strength and curvature. Considering
the spherically symmetric solution as an example we find the lowest order
corrections for the Reissner-Nordstr\"om metric and the electromagnetic field.
