  The electronic and magnetic structure, including the Heisenberg model
exchange interaction parameters, was explored for the recently proposed novel
cuprate Cu$_2$F$_5$. Using the DFT+U calculation, it is shown that the compound
is formed by two types of copper ions with $d^9$ and $d^8$ electronic
configurations. We have found a very stable antiferromagnetic ordering with
strong anisotropy of exchange interaction that results in the appearance of an
unusual 2D-magnetism: within the (100)-plane the exchange between the S=1 and
S=1/2 Cu ions has almost the same strength as between the two S=1 ions. The
interplane magnetic interaction is five times weaker than the in-plane one.
