Mike Walsh got to plug my Slacko 5.7.2CE before I could. But I could not have built it if it hadn't been for Sailor Enceladus' work.
It's impossible to swap a new kernel into an old Puppy. Using Slackware 14.0 binaries, 01micko published Slacko 5.7 in March of 2014. In or around October of that year, the team, lead by 01micko, working on Woof --the application used to build Puppies-- substantially re-arranged the components within each of the file systems which make up a Puppy: vmlinuz, Puppy_xxx.sfs and zdrv_puppy_xxx.sfs and modified initrd.gz to reflect those changes. As used here "old" means an original publication before October 2014.
In October of 2017, Sailor Enceladus used the then current Woof to built a new Slacko Puppy with Slackware 14.0 binaries.
http://www.murga-linux.com/puppy/viewto ... 794#976794. You can find several of his Slacko 5.7 and 5.8 Puppies here,
https://www.mediafire.com/folder/kwhxksubf00ny/14.0 and --IIRC-- links to some remasters by others on Sailor Enceladus' thread. [5.8 also uses Slackware 14.0 binaries. A remaster is not a new build. Rather, it starts with an already built Puppy and adds or deletes applications, or both].
Trying to use an "old" Puppy one can run into several hurdles among which are (1) it may not have the drivers and firmware needed to interface with hardware manufactured after the publication of the kernel used by that Puppy; (2) it's kernel WILL NOT include modifications since found necessary to avoid exploitations by malware; and (3) it may not include the libraries (infra-structure) needed to support new versions of applications.
The advantage of "old" Puppies is that the applications created to run under them will need less RAM: New Applications are built with the expectation that the user has a new computer with many gigabytes of RAM and fast processors and consequently is able to handle 'user-friendly/bloated" applications with whatever 'Bells and Whistles' an application's publisher could think of to 'enhance' an old version.
In general, an 'old' version of an application will run as effectively and productively on a new binary-compatible 'Puppy' as on an old; but it will lack those new 'Bells and Whistles'. There are two exceptions: Web-browsers and security protocols. Many current Websites generate graphic rich content which old web-browsers are not capable of displaying. Moreover, because of security concerns even more current Websites will not even allow you to obtain access if your Web-browser does not provide up-to-date security.
Over the last 5 years many applications were built to run OOTB under Slacko 5.7. They can be used under any of Sailor Enceladus' builds; or my remaster.
Slacko 5.7.2CE is a remaster of one of Sailor Enceladus' builds. It started with that but changed its kernel with one of the Real-Time Kernels rockedge published,
http://rockedge.org/kernels/. While providing patches against malware available when Rockedge created them, my experience was that these Real-Time Kernels appeared to be less RAM demanding and more responsive. After swapping kernels, I removed some applications, substituted others, but primarily I updated all "infrastructures" such as radky's improvements to the JWM desktop and rerwin's improvements to network modules.
If it matters, NO Slacko 5.7/5.8 can run any google-chrome (or clone) after version 48 which is now 3 years old and 20+ versions out-of-date. Slacko 5.7.2CE has built in all the infra-structure required by that latest firefox-quantum, firefox-esr, palemoon and Seamonkey.
Sailor's 5.7/5.8 should also be able to run those web-browsers. But I'm not certain whether you might have to first install the infra-structure the newest 'mozilla' web-browsers require. On the other hand, using one of Sailor Enceladus' Puppies may have an advantage. I don't compile, so I didn't take that into consideration. But I do know that in order to compile --such as creating a wifi driver-- an appropriate devx.sfs is required. You'll find any needed devx.sfs for each of Sailor Enceladus' Puppies on his repo. Associated with rockedge's kernels are "Kernel Sources".sfs. But I don't know if these include, or are sufficient, for compiling.