KöMaL 2022 B5222

Let $A$ denote the set of even positive integers for which the sum of the digits decreases by 2 if the number is halved. Let $B$ denote the set of positive integers for which the sum of the digits increases by 5 if the number is multiplied by 5. What is the number of elements in the set $A\cap B$ and in the set $B\setminus A$?