no not afaik. There is only counters per session. For uploads, you need to enable those column options in your Library. Right-click column bar heading & choose to show uploads & upload attempts & Hits. Hits is how often the files have been found in searches. Double-click the heading of each to find which files have been seen or uploaded the most, they will show at top of list.
For downloads, only can be seen via Download window. And depends on your settings. If you set them to clear then you will not see them after they complete. If not auto clear then you can check that window to see which ones are downloaded, mixed in with incompletes & presently downloading files.

Similar applies to LW 4. In both LW 4 & 5 you can set uploads to not auto-clear to see which ones uploaded. But unless you have many folders in your Library window, this method is not necessary.