Band structure calculations using the spin-polarized relativistic Korringa-Kohn-Rostoker (SPRKKR) band structure method have been performed to determine the intrinsic magnetic properties (magnetic moments, magneto-crystalline anisotropy -MAE and Curie temperatures) of the Fe5-x-yCoxMySiB2 (M = Re, W) alloys. The general gradient approximation for ex-change-correlation potential and the atomic sphere approximation (GGA ASA) have been em-ployed. Previous studies showed that the Co doping is turning the in-plane into axial anisotropy for a certain doping range, whilst the 5d doping enables a strong spin-orbit coupling of Fe-3d and M-5d states which is needed to enhance the MAE. The theoretical calculations aim to find the dependence of the anisotropy constant K1 for combined Co and M doping, building a two-dimensional (2D) map of K1 for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1. Similar theoretical 2D maps for magnetization and Curie temperature vs. Co and M content (M = W and Re) have been built, allowing to select alloy compositions with enhanced values of uniaxial anisotropy, magnetization and Curie temperature. Magnetic properties of Fe4.1W0.9SiB2 alloy that meets the selection criteria for axial anisotropy K1 > 0.2 meV/f.u., Curie temperature Tc > 800 K determined by mean field approach and magnetization µ0Ms > 1 T are discussed.