I do not like vegetables. The answer to this question relates not only to the recommendation regarding fruits and vegetables but also to the recommendation regarding eating a variety of foods. Many of them are especially rich in carotenoids, vitamin C, folate, and potassium.
Some specific vegetables are good sources of B vitamins, calcium and iron.
Some studies have pointed to green vegetables as being particularly important in breast cancer prevention. The answer to your question is that it is important for you to eat a variety of both fruits and vegetables, in fact it is probably ideal to try to include three servings of vegetables each day. The good news for you is that you may be getting vegetables in your diet that you are unaware of, such as tomatoes in tomato, spaghetti, or pasta sauce or tomato based soup. Also many soups, salads and mixed dishes contain a variety of vegetables and are good vehicles for adding more vegetables to your diet, perhaps in a more tolerable and inconspicuous way to you. Often people, including children prefer the taste of raw, rather than cooked, vegetables.