This would be a flat tax, which is a fair way to tax people from the perspective that each person is paying the same proportion of their income. There are also many people that believe that such a tax is not fair because the results of the tax are far more punishing to those with low incomes. This is a largely ideological belief based on whether you view equality of opportunity or outcomes as more important.
The biggest argument against a flat tax is that it is crippling to people that earn the least, taking 5% from someone just above the poverty line will force them into poverty and that isn't a desirable outcome, that will likely require some form of assistance from private charities or the government. A more progressive tax system would tax the bottom less and offset that loss by taxing the top slightly more. Depending on the difference in incomes between the top and bottom it can take an extremely small additional percentage of tax to replace that income. Since money has a marginal value its possible that the more money paid by the rich has less value to them than if it was paid by the poor. This is a double edged sword though, because by taxing the rich more it's possible to create a disincentive to increase income for high income earners since each extra dollar is both worse less to them and they receive less of each new dollar they earn. Progressive systems also run the risk of collapsing because they rely too much on a handful of people paying all the taxes, if even a small number of them leave then it becomes a massive blow to income.