This is a common problem and is caused by a Permissions issue between OS 10.9.5, LR and your external HD and is easily fixed. I have the same issue and it comes and goes for no apparent reason.
The simple workaround is -
Go to root level of the external HD and create a new folder (call it anything). Immediately delete the folder. This seems to fix the permissions conflict and trashing photos from LR should now work.
This should be fine though you may have to repeat the procedure after you've re-booted your Mac.
Hope this helps.
I've tried this, along with numerous other fixes on the forums and nothing seems to help. Running the latest version of LR (5.7) and Yosemite. It was not an issue before I upgraded to Yosemite though. I deleted files regularly using the typical tools/commands in LR with no problem at all. Most of the fixes have focused on problems with external hard drives but the files I am trying to delete are all on my hard drive. I also checked to be sure permissions were Read & Write on the main Adobe folder as well as the Lightroom folder in the finder.
This trick still works for me and I'm using Yosemite. Sorry, I don't know what else to suggest. The fact that the problem is with your internal HD is a new one on me. Anyone else got any ideas?
I spent a lot of time on the phone yesterday with LR help and they are stuck as well. They said they would get back to me and if they do come up with a solution I will post it. From what I could understand, there were some undefined issues related to Apple. It does seem to be quirky and not a global issues as only some people using LR5 and Yosemite are having problems.