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. 

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

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 -

https://support.turbotax.intuit.com/contact/ 

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?

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@noID4u wrote:

Neither of the links to Customer Service in this answer work.

What is a good link?

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Both of these TurboTax links are active -

https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632

And

https://support.turbotax.intuit.com/contact/

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)