Hmmm its quite funny that our nexus 5 is a bluetooth speaker for other phones xd. But ive have send a file. Just turn off on other phone music streamming to your nexus, an then use program, bluetooth file transfer. In this way i could send files to other phone. Not tested it in back way, i mean send file to nexus 5. U can do this and inform us :D. It should work, you can read this feature in app.

If you go to Github.com you can create an account there and then go to issues and raise another. When creating it gives you the option to ađdo issue or new feature.