Yes to both questions. The income limit you refer to is based on taxable income, in other words, AGI (which includes the capital gains) minus allowable deductions (whether the standard deduction or itemized deductions). Capital gains are considered to be on the "top"of that heap, in other words, considered last. Thus, using your example, your taxable income before capital gains is $73,750, and you have $10,000 of long-term capital gains. $5,000 of those gains will be taxed at 0% (up to the $78,750 line), and the remaining $5,000 of capital gains will be taxed at 15%.
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