I am guessing that you can't use a flash drive because there are no USB ports on the older machine. Otherwise, find the driver software for the older computer's OS and install it. Then use the flash drive.
You should be able to use WinZip (or another file compression program) to create a Zip archive that spans multiple floppies. (I remember doing that with PAF 4.0. years ago.) Select the floppy drive as the destination for the Zip archive and follow the prompts. Then run the unzip routine to rebuild the installer on the second machine.
You may also be able to use one of the free file splitters to split the PAF5 installer, so it can be copied to multiple floppies, and then recombined on the second computer.
I believe PAF4 can run in 32 MB of RAM, but PAF5 needs 64 MB. PAF4 can run on a late release of Win95. A computer like the one you are describing may not meet the modest hardware requirements of PAF.
Personally, I would try the Zip archive route, and if it didn't work, try the file splitter.
If you know what you are doing, you could unplug the DVD drive on a newer computer and connect the 1GB HDD in its place and copy the installer to the HDD. Then put the HDD back in the original computer and run the installer. This is not fool-proof, as jumpers on the HDD might need to be reset.
Of course, if you know someone who has an old Iomega Zip drive, that would be a better alternative than doing a drive-swap. I haven't seen one for a long time, but found them very handy about 10 years ago. It would probably need to be the parallel port version.
I hope one of these suggestions will help you to solve the problem.