3 is absolutely not nutsedge. Not remotely close. (Be glad.) 5 is definitely buttonweed. You have my sympathy. I've read that the best way to control it is to tear it out whenever you see it, and mow short.

Do they bloom with a yellow head? Sorta look like goldenrod.

The flowers on the second plant really look like ragweed flowers to me. 8 feet tall could be Giant Ragweed, Ambrosia trifida. The leaves I can see in the photo don't look quite right, but a larger image should make it clearer. Or it could be a different species from the two common ones I'm familiar with. USDA lists a bunch of species and I don't have time to go through them now. On a side note, while looking for this I went to the Dan Tenaglia's old Missouri Plants website and discovered that the Missouri Botanical Garden has taken it over and is updating it. That site was the first wildflower ID site I found on the internet back when all this was pretty new and was a real inspiration to me about what you could do along those lines, as well as being a very useful ID tool. It still is, for that matter. I'm really glad it's being continued. WW

Some sort of weedy allium, maybe Allium canadense, wild garlic.