First, export your current bookmarks in HTML format to a safe location such as your Documents folder or Desktop. See: Export Firefox bookmarks to an HTML file to back up or transfer bookmarks. This is crucial to keeping your bookmarks from the past 5 months.

Now... I'm not sure I completely understand what you have available to restore from such as a backup from around June 13th. Do you have some kind of backup file or are you looking for suggestions about where to dig one up?

Firefox normally creates a small number of dated backups, and they show up in the Library dialog on the Restore menu. This article describes how to check that; perhaps this is what you already checked: Restore bookmarks from backup or move them to another computer.

Unfortunately, those files are not kept forever, as newer ones are created, older ones are deleted. If you need to find something older, here are some thoughts:

(1) If you have ever used the Refresh feature, there should be an Old Firefox Data folder on your desktop (assuming you haven't deleted it). If you have such a folder from the Summer, check inside to see what bookmarkbackups folders you can fine.

(2) Windows often creates "restore points" when you do monthly updates. While it is difficult to search though restore points using the built-in features of windows, you could try a program like the following (I haven't tried it myself):

http://nicbedford.co.uk/software/systemrestoreexplorer/

You would be looking for any files with names starting with:

• bookmarks-2015-06 ...
• bookmarks-2015-05 ...

Are you able to dig up anything useful?

Please note that the Restore feature will completely replace all your existing bookmarks and roll you back to the earlier date. That's why the first step is to export to HTML format. To then add those back after the Resore, you can import the HTML file and then reorganize. This article should help with that:

Import Bookmarks from an HTML file

When did you lose these bookmarks?

Was that recently or quite a while back?

The name of a JSON bookmarks backup file includes a total item count (folders and separators included) and an hash value to prevent saving the same backup more than once. If I happened recently then you can check the name for a sudden drop in the count.

• bookmarks-YYYY-MM-DD_<item count>_<hash>.jsonlz4.

Also make sure that you haven't moved bookmarks accidentally into another folder. You can try a search to be sure.