I will try not to take anything you said out of context.
You are out of a job and need money, but you are already complaining you don't want to do certain jobs. To me that means you aren't hungry yet. Hungry enough for either money or work.
Now if they are asking you to mow the lawn for $5/hr, I would then agree with you, way too cheap. You arent doing charity work.
But again, if you have no money, $5/hr is better than sitting here on the internet complaining you need money.
If what you say is true about these neighbors. They will nit-pick your work, and you may not even get paid. Be careful. Every neighborhood has "that one neighbor".
How much to charge? Look at what the lawn care places are getting. Are you providing your own equipment? Are you bonded and insured? Lots of unanswered questions. You are worth more than $5 hour doing yard work in my opinion. But if it was the only work you have, I would take it.