NavigableMap<Integer, String> map = new TreeMap<>();
// code to fill my map with values from 1 to 20, key=int, value=String.valueOf(int)
IntStream.rangeClosed(1,20).forEach(i->map.put(i, String.valueOf(i)));

NavigableMap<Integer, String> subMap = map.subMap(5, false, 10, false);

subMap.forEach(
    (k, v) -> System.out.println("Key: " + k + ", value: " + v)
);