Not sure I totally understood your explaination of your network, but I think you were saying you were replacing your 3750 with N5K, which will link to a 6500 core? (if I am incorrect, please feel free to clarify).
The Nexus5548 is a layer two switch, in other words it has no capacity for routing. Although this will change with the L3 daughter card for the 55XX being released next year, at this moment in time the switch is purely layer 2, in other words you can't run HSRP or OSPF on an N5K. You would need to move your HSRP up to the 6500, and make that your hosts default gateway.
You can then connect your 5548 via an L2 link to your 6509, standalone, portchannel or vPC (providing you have a second 5548).
You can of course have VLAN interfaces to access the N5K management purposes, but from a traffic forwarding perspective (as it is a L2 switch rather than an L3 switch) your 6500 would talk "through" it rather than "to" it.
Hope this clarifies.