The headaches are almost certainly caused by 2 factors:
Lack of caffeine if you're a big caffeine junky (that'll go away with time though - it's good to "detox" from caffeine every now and then)
And more importantly: protein deficit - this will do very bad things for your health if kept up longterm. 5 days won't cause anything serious though, and if you're doing this just for a challenge or to try something new that's cool but I would caution against keeping up such a diet for a long time.
Apart from the obvious functions of protein in the body (building blocks of muscle and other organs), the amino acids are essential to neurotransmitter function and you can end up with severe mental health issues if you don't get enough aminos.
I'd recommend you try some of those amino acid pills or a bit of whey protein extract mixed in with your juices. Whey is a pretty good source of protein and there's all sorts of products on the market that mix it with some really nice flavours.
Of course you will still get some amount of aminos from the fruit and veg, but it's not really in sufficient amounts to keep you going. Personally I have a protein bar or a Huel drink (see http://huel.me and read my post here on powdered foods - it's awesome) for breakfast most days alongside a multivit, a time-release B complex and some fish oil capsules.
Then I throw a bunch of drugs on top of that - delicious cognitively enhancing drugs (piracetam and modafinil, mmmmm), but that's not something I can really advise most people to take for obvious reasons.
I will say though, some of those juice recipes do look quite awesome in terms of both taste and nutrition - just not as a sole dietary intake!
The apple especially is a good one for the mornings, malic acid is a nice little compound that can replicate some of the stimulatory effects of caffeine without the side effects of cardiac risk and addiction and I often stack it as an ingredient in my own homebrew energy drinks (alongside the usual combo of caffeine, B vitamins and aminos).
Great feedback @garethnelsonuk :)
I also agree this is not a long term solution, this is an intermittent fast and not something i would ever recommend as a full time diet option. That's the reason for the abundance of Romaine in my juices, they are amazing and very under used. Romaine lettuce’s calories are 20 percent protein. Like all whole foods, much of this protein is complete, but the amount can be increased by combining with balancing proteins. They also contain oega 3 and 6 and are alakaline forming. Sure not much of them is fat but simply no reason not to include them.
However i would encourage people to replace a meal with a juice as an ongoing thing. As you say above the nutrition hit from just one of these is simply hard to beat.