  We construct a new exact solution in the 5D Einstein-Maxwell-dilaton gravity
describing a magnetized squashed black hole. We calculate its physical
characteristics, and derive the Smarr-like relations. The Hawking radiation of
the solution is also investigated by calculating the greybody factor for the
emission of massless scalar particles in the low-energy regime. In distinction
to the case of asymptotically flat magnetized black holes, the thermodynamical
characteristics and the Hawking radiation of the solution depend on the
external magnetic field, and consequently can be tuned by its variation.
