As noted, the amount you can claim as a deduction for items of tangible personal property that have increased in value is your original cost, not the current fair market value. The only time a donation of baseball cards would have a deductible value equal to the present fair market value is if you donated them to a museum or similar charity that would keep them as cards (keep and use them for their intended purpose) for their charitable purposes. If the charity is going to sell the items, your deduction value is limited to your original cost. You may be better off selling them yourself, reporting and paying the capital gains tax, and then donating some or all of the money.
And naturally, you would need records of your original cost if audited, and if you claim a value of more that $5000 even for the original cost and not the FMV, you need an appraisal. (The appraisal might say the current FMV is $15,000, but you would still only claim your cost if that was less.)
See publication 526, under "donations of property that have increased in value."
https://www.irs.gov/pub/irs-pdf/p526.pdf
