Starting with the cylinders around arbitrary minor axis, as a whole you've done a pretty good job with these. Your linework is confident, your ellipses are evenly shaped, and your alignments are pretty accurate across the whole set. I'm also pleased to see that you're very conscientious in checking those alignments, identifying the "correct" minor axes even when they're only slightly off from what you were aiming for.
I did notice one small issue that came up on occasion. The foreshortening of your cylinders manifests in two separate ways. One is in the shift in scale, where the far end is smaller than the closer end. The other is the shift in degree, where the far end is wider than the closer end. These two 'shifts' need to be applied in roughly equal measure - meaning that if you have a more dramatic shift in scale, you have to match it with an equally dramatic shift in degree. We're not talking about being hyper accurate - just avoid situations like this where you've got a significant shift in scale, but a minor shift in degree, or vice-versa. This results in a visual contradiction, where one element tells the viewer that there's dramatic foreshortening on the form, and the other tells the viewer that there's shallow foreshortening.
Continuing onto your cylinders in boxes, as a whole you're not doing badly here, in that you're doing a great job of checking your line extensions fastidiously throughout the set. The key point to keep in mind here is that from page to page, we want to be altering how we approach drawing the boxes themselves, based on what the line extensions from the previous page tell us. The exercise as a whole is intended to develop your instinctual awareness of how the box should be drawn to maintain two opposite faces which are proportionally square.
We work towards this by using the cylinder - or its ellipses - as a further development of the line extensions from the box challenge. We know that when the ellipse's lines (the minor axis and the contact point lines) converge towards the box's own vanishing points, those ellipses represent circles in 3D space which rest on the surface of that box. This also tells us that the planes that enclose these circles in 3D space are themselves squares in 3D space.
Now, the overall point is that I don't think you're necessarily pushing yourself to make those kinds of alterations, at least not with enough boldness or confidence, and so while you do make progress over the set, it's somewhat more gradual and tentative. When practicing this exercise in the future, I recommend that you try to make more meaningful changes to how you construct those boxes - don't be afraid of overcompensating, only to find that the line extensions say you went too far. That's totally normal - you'll just correct again in the opposite direction, getting closer and closer, all the while fleshing out your brain's understanding of how these proportions function with all the other variables of 3D space.
All in all, your work here is still coming along quite well. You've got a few things to keep in mind, but you're good to consider this challenge complete.
Next Steps:
Feel free to move onto lesson 6.
Where the rest of my recommendations tend to be for specific products, this one is a little more general. It's about printer paper.
As discussed in Lesson 0, printer paper (A4 or 8.5"x11") is what we recommend. It's well suited to the kind of tools we're using, and the nature of the work we're doing (in terms of size). But a lot of students still feel driven to sketchbooks, either by a desire to feel more like an artist, or to be able to compile their work as they go through the course.
Neither is a good enough reason to use something that is going to more expensive, more complex in terms of finding the right kind for the tools we're using, more stress-inducing (in terms of not wanting to "ruin" a sketchbook - we make a lot of mistakes throughout the work in this course), and more likely to keep you from developing the habits we try to instill in our students (like rotating the page to find a comfortable angle of approach).
Whether you grab the ream of printer paper linked here, a different brand, or pick one up from a store near you - do yourself a favour and don't make things even more difficult for you. And if you want to compile your work, you can always keep it in a folder, and even have it bound into a book when you're done.
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