Q. If for example that person purchased the shares at $10 and sold at $15, is the 'gain' on each share $5 for the purpose of paying capital gains tax in the year of sale?
A. Yes.
Q. Or is it more nuanced than that, where the capital gains they paid each year somehow has to come into the calculation?
A. No. Since you did not use those capital gains distributions and dividends to purchase additional shares. If you had purchased additional shares, those additional shares would have a different cost basis than the original shares. You would be expected to keep track of that cost basis (in most cases the fund does that for you, usually using the cost averaging method)
