Be responsible, think of your child, you will be fine

Share the infinancial information with your wife and lay out a plan for savings, such as your (including her) retirements, kid's education fund, saving to buy a new and bigger car and saving to buy a bigger house etc , she will understand. After all, she has no motivation/intention to break the family: It would be really hard for her to marry another man, or would she want to raise the child by herself?

$5,000/month is good enough for your family to go a long run. You should be able to aford organic foods (you only need organic meat, eggs and diary products, no need to go with orgnic fruits and vegetibales. And you can always find on sale stuff, for example, in Whole Foods in MA, organic drum sticks only cost $0.99 per pound when they are on sale).

If you don't believe, I can be a small example for you. When my first child was born, my wife was not working (she never went back working) and my monthly income was only about $3,200/month. We didn't even go to a fast food resturaunt for more than a year. I worked hard to get more money, and my wife tried hard to save. Now we not ownly own a house, we also have several investment properties. Comparing with me, you at least have a better starting point.

Don't take divorce lightly. You are a man, you are responsible for the family, at least for your own child's benefit. Talk to your wife honestly(but with some tactics) and work hard with her together,  you will be a big man.