Should I connect the computer VBUS line to the 5V line of the board?
If your board has it's own power, the VBUS from upstream connector should NOT be used as power source and should NOT be connected to the +5V rail. It will cause unpredictable conflict between your on-board power source and USB host-supplied VBUS.

However, your device must have a circuitry (typically a GPIO input with proper level translation and additional ESD protection) to sense the VBUS presence. This function is defined in Section 7.1.5.1 of USB 2.0 Specifications,


  The voltage source on the pull-up resistor must be derived from or
  controlled by the power supplied on the USB cable such that when VBUS
  is removed, the pull-up resistor does not supply current on the data
  line to which it is attached.


and further explained in Section 7.2.1, p.171:


  They [devices] may not provide power to the pull-up resistor on D+/D- unless
  VBUS is present (see Section 7.1.5). When VBUS is removed, the device
  must remove power from the D+/D- pull-up resistor within 10 seconds.


If you have a concern about pin5 on ESD protector U10, then it would be the best to keep this pin at 3.3V form some internal rail, it will provide somewhat better level of protection. 

There are more answers on this topic, like here.