Je dois encore le travailler mais c'est un début de réflexion.

Objectif : utiliser la classe de cette manière :

RomanNumber toto = new RomanNumber(5);
System.out.println(toto.toString());

Dans le cas ou l'on souhaite une représentation textuelle, bien sûr.

import java.util.LinkedList;
import java.util.List;

public class RomanNumber {

    private List<RomanCharacter> characters;

    public RomanNumber(int arabicNumber) {
        this.characters = new LinkedList<>();
        this.convertArabicNumberToRomanNumber(arabicNumber);
    }

    private void convertArabicNumberToRomanNumber(int arabicNumber) {
        int remains = arabicNumber;
        for (RomanCharacter currentCharacter : RomanCharacter.getOrderedRomanNumbers()) {
            while (this.arabicNumberIsGreaterThanRomanNumber(remains, currentCharacter)) {
                this.characters.add(currentCharacter);
                remains = remains - currentCharacter.toInt();
            }
            if (remains == 0) {
                break;
            }
        }
    }

    private boolean arabicNumberIsGreaterThanRomanNumber(int arabicNumber, RomanCharacter romanNumber) {
        return arabicNumber > 0 && arabicNumber >= romanNumber.toInt();
    }

    public String toString() {
        StringBuilder textualVersion = new StringBuilder(this.characters.size());
        for (RomanCharacter character : this.characters) {
            textualVersion.append(character.toString());
        }
        return textualVersion.toString();
    }
}

import java.util.*;

public enum RomanCharacter {
    M(1000), CM(900), D(500), CD(400), C(100), XC(90), L(50), XL(40), X(10), IX(9), V(5), IV(4), I(1);

    private final int correspondingArabicNumber;

    RomanCharacter(int arabicNumber) {
        this.correspondingArabicNumber = arabicNumber;
    }

    public int toInt() {
        return this.correspondingArabicNumber;
    }

    public String toString() {
        return this.name();
    }

    public static List<RomanCharacter> getOrderedRomanNumbers() {
        return Arrays.asList(RomanCharacter.values());
    }

}