public abstract class X  {
    public abstract void commonFunction();
}

Map<String,A> mapA = new HashMap<String,A>();
Map<String,B> mapB = new HashMap<String,B>();
Map<String,C> mapC = new HashMap<String,C>();
Map<String,D> mapD = new HashMap<String,D>();
Map<String,E> mapE = new HashMap<String,E>();

someFunction(mapA); // or someFunction(mapB) etc.

void someFunction(Map<String,X> mapX) {
    ...some stuff
    x.commonFunction();
    ...more stuff
}