What's error 345 with HPOfficejet j5780 all in one while faxing?

SOURCE: FAX errors 345 346 and 350

HP.com has a web page for your product with all of the fax error codes listed and how to interpret them:

Fax Error Codes

Once the page opens, you'll have to scroll down until you find your error codes in the list. The codes in that section of the page don't seem to line up well. All of the codes have to do with the quality of service on the phone line. If the people you're faxing to are receiving all of their faxes except from you, I'd suspect your phone line may have a problem. Here's what I got from the list:

The remote machine has failed to respond to a fax command from the local machine due to the connection being interrupted. These errors can occur if the phone lines in the area to be faxed are old or there is noise (static on the phone line). Other reasons can include power outages and other power related problems.
OR
The call waiting service can cause this error. The click, heard for an incoming call, is actually a momentary disconnect of the line.
OR
The remote user has pressed the Stop key while the reception was in progress.
OR
Under rare conditions incompatibility between the two machines may cause the remote machine to simply abandon the call.

Check with your phone company to see if their are any problems on your line. It looks like anything that even momentarily interrupts your phone connection will cause these errors. Good luck.