Rich,
I don't know where you got your Slackware package to install or if you created it yourself, as I do. Or you installed the RPM directly. I use SlackBuilds.org for my Slack packages. Here is S14.1 LO 5.1.4:
https://www.slackbuilds.org/result/?search=libreoffice&sv=14.1
There is a link to the LO website where you can download 5.1.4. Alas, it is no longer available or broken. I did some drilling work for you and here is 5.1.6 on a mirror site, which is supposed to be the stable version:
http://ftp.ussg.indiana.edu/tdf/libreoffice/stable/5.1.6/rpm/x86/
Another point is that I was told that the most stable LO is x.x.6+. Since 5.3 is not there yet, I will wait until 5.3.6 is released or try 5.2.6. I am currently running LO 5.1.6.2 on My Slackware 14.2 system. Like you, it runs fine.
I also am confused as to why you seem to have lost fonts in /usr/share/fonts. You are not running LO as root are you? That path and all the files in there should only have root write permissions. Running LO as a user should not remove fonts from that directory. I have not looked at 5.3 yet, so I do not know what the distribution package would overwrite when installed as root. I always look at the package innards before I install it to see if there are any nasties in there which could cause problems. I have been burned in the past by packages that do nasty things. I just looked at my LO 5.1.6.2 Slackware package that I created and there is no /usr/share/fonts directory, so it could not overwrite anything when installed.
Alas, reinstalling LO 5.1.4 will probably not restore your missing fonts. Good luck.
HTH.
Girvin Herr