By the way, the reason you kept seeing the same version of firefox open is probably because all other instances of (the older) firefox were not closed completely first. Newer versions have a "-no-remote" switch so that you can have multiple versions open simultaneously.

And yes, new versions of Firefox will not work out of the box on old versions of Slackware. It wouldn't work on old versions of Ubuntu either until you upgraded tons of libraries (much more in fact than you would probably have to for Slackware).

I recommend migrating your important files to a recent version of the distro of your choice- whether that be Slackware or not.