You will have to make a good-faith effort to estimate the date you purchased those securities and the cost basis. For cost basis, don't forget add any dividends you may have reinvested over the years. They should already have been taxed - adding them to the cost basis will reduce your gain on the sale (or increase your loss).
If you believe it was long term transaction, enter a date that is at least 1 year earlier than the date you sold the security (e.g. 12/31/2015). As long as the program sees you held the security for at least 1 year before selling it, the gain (or loss) will be properly characterized.
If you believe it was a short term transaction, enter a date that is at less than 1 year before the date you sold the security (e.g. 01/05/2016). As long as the program sees you held the security for less than 1 year before selling it, the gain (or loss) will be properly characterized.
