Should I be responsible for the taxes if I was a stay at home mom?

My ex husband and I divorced 5 years ago. He received a letter from the IRS saying we owed thousands of dollars in taxes. He came to me last year and demanded that I pay him half of what we owe. I told him I thought he paid the taxes since he put in the papers NO TAX LIABILITIES, and I also stayed home with our two children while he worked. He is only coming to me for the $ because 5 years ago we each got a settlement from the sell of our home, and I invested mine and he spent all his. I would love to hear what you all think.