Libreoffice fails to integrate with unity

I assume that you upgraded manually, using the installation file from LibreOffice.
But you should wait until LibreOffice 5.1 is available in the LibreOffice Fresh PPA.

This usually does not take a very long time after a new LibreOffice version release.
When you do it this way, integration with the Ubuntu Unity menu bar will work fine.

To add the LibreOffice Fresh PPA to the repositories, open a terminal and execute :

sudo add-apt-repository ppa:libreoffice/ppa  
sudo apt-get update

When the new LibreOffice edition arrives - you can upgrade to version 5.1 as usual :

sudo apt-get upgrade

LibreOffice PPA description : This PPA will have what the Document Foundation calls "LibreOffice fresh", the latest release of the newest series (but no alpha/beta releases).

LibreOffice 5.1 release notes : This is the first release of the 5.1.x branch of LibreOffice which contains new features and program enhancements. As such, the version is stable and is suitable for all users. This version may contain a few annoying bugs which will be fixed in the next bugfix versions to come ... so, you may want to consider waiting until LibreOffice 5.1.1 will be released.

Update information 2016-02-23 : LibreOffice 5.1.0 is now available in the LibreOffice Fresh PPA.
LibreOffice Unity integration works in Ubuntu 14.04.4, but it still does not work in Ubuntu 15.10 !

Update information 2016-03-02 : LibreOffice 5.1.1 is now available in the LibreOffice Fresh PPA.
The issue is fixed and LibreOffice 5.1.1 integration with the Unity menu bar works flawlessly now.

Maxim Monastirsky in bug#97830 gave a solution, cite: "Remove the libreoffice-gtk3 package.". For me it did the job in ubuntu 15.10 x64 and libreoffice 5.1.0.3.