rdz4No, not unless you're setting up an entirely new system.
The Q5 is a DAC/Integrated amp combo without the line-level analog outputs you'd need for it to be of any use with the LSR305. The LS305s are powered monitors which already have their own built-in amps.
With the LSR 305s you really just need a DAC and, unless you want to have to adjust the volume on the back of each speaker individually every time you want to change it, some sort of volume control (preferably a passive preamp, like the JDS Labs OL Switcher or Schiit Sys).