Both figures are true.
The top 5 percent of all payers do pay more than half the income tax. They pay about 59.2 percent of all individual income tax, according to an analysis by the Tax Policy Center, a nonpartisan institute run jointly by the Urban Institute and the Brookings Institution.
Thompson also said that 40 percent of Americans pay no income tax. This claim is supported by the Tax Foundation, a nonpartisan tax research group that promotes transparency in the tax code and economic growth.
There's a small caveat to the 40 percent number — it includes nonfilers, typically taxpayers who don't have to file returns because their incomes are too low. It's logical to assume that most nonfilers don't pay income taxes, but it's possible that some did if they had income taxes withheld by an employer. This is probably a very small number, because people with low incomes have an economic incentive to file a return and get a refund.
The U.S. income tax system is progressive, which means that rates increase as income increases. Given that structure, it makes sense that people with higher incomes pay more taxes, and people with low incomes might pay no tax at all. Thompson's numbers are on the money, and we rate them True.