Are you sure there's no 6 pin power cable in that machine? I'm not there to look.
http://www.newegg.com/Product/Product.aspx?Item=N82E16812816038 for example.
Hopefully you have 2 SATA power connections.
So I recently bought a GTX 1050 Ti. It fits into my desktop but it comes with Power Cables that do not plug in to anywhere in my computer. The cables are the supplemental power cable and it is required for me to start up the computer using the 1050 Ti. My computer is a little outdated and has the plugs for cable supplements but they are way to small to plug in the Ti's power cable. Can I buy an adapter anywhere or what can I do to fix this problem?
P.S: This is what the computer's power supply cables look like.