The Apple system requirements states explicitly, when using the iMac 27" mid 2010 as a target display a Mini DisplayPort to Mini DsplayPort cable connected to the iMac 27" Late 2015's Thunderbolt port (in your case).
iMacs you can use as a display |
Cable you need |
Port you need on your other Mac |
iMac (27-inch Mid 2010) |
Mini DisplayPort to Mini DisplayPort |
Mini DisplayPort or Thunderbolt |
Apple does not sell such a cable. Comments on Apple Store site about using Thunderbolt cable confirm that Thunderbolt cable does not work.
This should work
http://www.belkin.com/us/p/P-F2CD008/
Please, also note that
iMac (Retina 5K, 27-inch, Late 2014) and later iMac models can't be used as Target Display Mode displays