You can get the 2015 download by contacting customer service. You paid for 2013 they will send 2015 for the charge you have already paid.
To contact TurboTax customer service/support use their contact website during business hours.
Submit your question/problem during business hours and then use the option for Call (a phone number will be provided for Call) to speak directly with a TurboTax agent -
Note: The Call option will not be available when TurboTax Support is closed.
Neither of the links to Customer Service in this answer work.
What is a good link?
Both of these TurboTax links are active -
If you cannot access support using those links, close the TurboTax window. Clear cache and cookies on your web browser. Close the browser. Re-open the browser and access the support links again.
If the problem persists, change your web browser to either Google Chrome, Mozilla Firefox or Windows Internet Explorer (Not Edge)