Not really, because the human body requires fat to function. It doesn't require carbs. Carbohydrate is the only nonessential micronutrient - everything it gives your body (ie: glucose) your body can also get efficiently from fat and protein.
I've been eating under 30g carb daily for nearly a year now. It's not always easy, the modern world throws a lot of carbs in our faces and nearly all convenience foods are carb traps. But it's very doable with no ill effect. I can also eat a ton of veggies: asparagus, spinach, broccoli, courgette, cauliflower, tomato, mushroom, rhubarb - all whole keeping my carbs at this level. I often have wholly veggie days.
It sounds to me like you're not getting past the initial glycogen depletion stage. It's very normal to feel rubbish after 5 days. It takes a few weeks to get settled - sometimes a little longer. But for me personally it's the highest energy, fastest weight loss method I've tried.