Five-Dimensional Lax-Integrable Equation, Its Reductions and Recursion Operator

We consider a five-dimensional nonlinear PDE associated to the five-dimensional equation introduced by Martinez Alonso and Shabat. For our equation we find differential coverings with non-removable parameters and list its reductions to known 4D and 3D integrable equations. One of the coverings produces a new family of integrable 5D equations. We show that each pair of these equations is related by a Backlund transformation, including the Backlund auto-transformation for each equation from the family. Also we find a recursion operator for symmetries of the equation and study its action.