When I lived in suburbia, I felt incredible pressure to have a "good lawn" and zero "conventional weeds" anywhere, especially since I always had a lot less lawn, and many more flowers, than most houses. In neighborhoods where a good lawn is a priority, the paltry amount it costs for a service might be worthwhile in terms of the property not being labeled as "needs new sod" at the point one might want to sell later, especially if it is a very large lawn. When we lived in a golf course community, of course you're supposed to have a good lawn. I mean it's in the HOA. I'm sure there are a lot of plants I don't want about which others would rhapsodize, with much more traditionally pretty flowers. Just trying to encourage people to think for themselves and make their own decisions if they've found themselves at some point wondering why they're paying or spending time to get rid of plants they do like, or why it's "necessary" to only have grass in the mowed areas. There may be an objectively valid reason, there may not. I became so curious about the whole thing a few years back, I bought a couple books to satisfy my curiosity about why we even have lawns, where the idea came from, and how to be a property owner/tender without devoting so much of my life tending something about which I'm ambivalent. As long as there's enough room to play with the kids and grill some burgers, the way I see it, the rest of the area being mowed is wasting my time, my money in gas to run and maintain the mower, and doing virtually nothing beneficial to nature. At one house, I had the lawn down to 20 minutes of mowing. But if it makes someone happy to look over 5 acres of freshly mowed lawn, more power to ya! If the HOA says no weeds allowed, not much option there. Admit, it's a lot easier to be non-chem when the property is so much smaller, a lot easier indeed.

Hi, It looks like the weedy nightshade(solanum) plant I'm always finding. Smell the leaves. They will smell bad if it is the plant I'm talking about. Remy

The flowering plant looks like dayflower, Commelina communis. There are other species of dayflower--check Google and Google Images. It's hard to be sure without seeing the flower. It's an awful pest. My sad story is that I begged my Philadelphia SIL for a piece of this because I remembered a nicer version from my grandmother's garden. She warned me what a weed it was so I never planted it but it colonized part of my garden just from a paper bag on the deck. Hope I'm wrong about the ID of your plant.

First is Jewelweed. Really good for butterflys and hummers. Also great to spread on your skin if you get poison ivy. Always try on your skin before using to see if you have a problem with the gel. Second is a type of dock. Use a long knife and cut the roots way underground. If the root turns yellow it is similar to the burdock that you can purchase in many grocery stores. 3 I am not certain but appears similar to Virginia Bluebells. However you have a much worse problem at the base of the picture, vinca. Vinca will take over everything including climbing trees and will with time be the only plant there. We have it across the street and other than providing cover for a few creatures there is no use for it. 4-5 Your plant may be lesser celadine because you mention flowers. Rather than getting rid of the things you have pictured most would be trying to divide to have more to plant.