Let's say someone just sold some stock and their total gains on that stock were $5,000. At what time do they have to cut the U.S. government a check to pay the taxes on this gain?
Let me clarify: I'm not asking about how MUCH they have to pay. I know this depends on their tax bracket and how long they have held the stock for.
I basically want to know if they have to cut the government a check ASAP or just wait until next year's tax returns are due.
It kind of depends on what they had to pay (or get back) with the previous year's return. Generally speaking, the average person gets 1 year of 'safe harbor' to get this wrong. That is, if at the end of 2017 and you compute and file your taxes in April of 2018, you find you owed a great deal of money (because say, relevant to this question, they had a lot of capital gains), the government will usually not fine them for not paying taxes on that throughout the year.
However, going forward, the government will be far less lenient about this; the IRS expects you to pay-as-you-go. And if the person this next year continues to earn significant income from capital gains, the government will expect them to estimate that income and make quarterly estimated payments with the goal of not having to owe anything when you file that year's taxes.
"Generally, most taxpayers will avoid this penalty if they either owe less than $1,000 in tax after subtracting their withholding and refundable credits, or if they paid withholding and estimated tax of at least 90% of the tax for the current year or 100% of the tax shown on the return for the prior year, whichever is smaller." https://www.irs.gov/taxtopics/tc306
Best advice is to consult a tax professional.
I am assuming the capital gains was becasue you sold a stock in 2018, and that this is a one-off event.
Then safe harbor rules our your friend to avoid the underpayment penalty:
Who Must Pay the Underpayment Penalty
In general, you may owe the penalty for [2018] if the total of your withholding and timely estimated tax payments didn't equal at least the smaller of:
90% of your [2018] tax, or
100% of your 2017 tax. Your [2017] tax return must cover a 12-month period.
Higher income taxpayers.
If your adjusted gross income (AGI) for [2017] was more than $150,000 ($75,000 if your [2017] filing status is married filing separately), substitute 110% for 100% in (2) above.
So if you can adjust your withholding on your wages by decreasing the number of allowances, or by having extra money withheld from each paycheck, tom make the safe harbor, then it doesn't matter how much the capital gains is, there will be no penalty next April. Making sure you make the safe harbor means that you can avoid the quarterly tax payments, and having to calculate the expected capital gains now with more than 6 months left in the tax year.
Now for the bad news. In calendar year 2019 you will have to either make the higher safe harbor again by keeping the higher withholding or make sure that you don't owe more than $1000 in April 2020.
Some years ago when I sold a property with a large capital gains, I made the adjustment to my withholding to make sure I made the safe harbor. Then I made a payment of over $10K to the IRS with my tax return. There was no penalty. Of course I had to be careful that I didn't owe a large amount the next year by making sure I over withheld.
In no case would you have to send the government a check "ASAP". If you don't expect to meet the safe harbor provisions described in the other answers, the simplest method would be to file an estimated tax form (1040-ES) on the next (approximately quarterly) due date, and send them a check then. You can find instructions on the IRS web site.
Alternatively, if you have a job where you have tax withheld, you could adjust the withholding amount to put you within the safe harbor amount. I think this is more complicated, unless you expect capital gains to be a recurring event with predictable amounts.
