Do I need the Ground and 5 V pin connect to Led?
I think it is not a good idea to power the LED strip via USB.

Normally USB delivers a maximum of mA  (see below). Assuming you have 30 LEDs (minimum for a normal LED strip), and each LED gives 40 mA (maximum), this is already more than what most USB ports can deliver. This can ruin your USB port.

For the Arduino Nano you can use the 5 V, and you should connect all GNDs together.

But you will need a decent adapter anyway for the LED strip, so than you can power your Arduino Nano from the adapter you use for the LED strip.

Update

According to Wikipedia USB power


  Low-power devices (such as a typical USB keyboard) may draw at most 1
  unit load (1 unit load is 100 mA for USB devices up to USB 2.0, while
  USB 3.0 defines a unit load as 150 mA), and all devices must act as
  Low-power devices when starting out as unconfigured.
  
  High-power devices (such as a typical 2.5-inch USB Hard Drive) draw at least 1 unit load and at most 5 unit loads (500 mA) for
  devices up to USB 2.0 or 6 unit loads (900 mA) for SuperSpeed devices.