Your question relates to being a retiree with an income under $47250 and anticipating a large long-term capital gain, in excess of $500000, from the sale of a family business in 2025. This sale will go on your 2024 tax return so my answer will be using capital gains rules for 2024. You do not indicate if you are married or not so I will discuss both scenarios.
With the additional capital gains income, 85% of your social security benefits will be taxable. If your 2024 social security benefits are $47250 the taxable portion will be 85% or $40163. That with your capital gains will give you a taxable income in excess of $540163.
For 2024 a single filer with taxable income of $540163 would have their capital gains taxed at 20%. If your capital gains are $500000, the tax on those gains will be $100000. However, if those gains are from the sale of section 1202 qualified small business stock, they may be taxed up to 28%, which would be $140000.
In 2024 a married filer with taxable income of $540163 would have their capital gains taxed at the 15% rate for taxable income up to $553850. 15% tax of the $500000 capital gains would be $75000l however, the section 1202 qualified small business stock rules may still apply.
Here is the link to the IRS info on capital gains and losses. You'll also be able to find more information on section 1202 qualified small business stock if necessary. https://www.irs.gov/taxtopics/tc409
