Is it still possible to install Debian 5 in 2018?

I would like to install Debian 5 on an older PC, because Debian 5's kernel should work well on this computer.

Umm... no!

That is in fact a Really Bad Idea. There are multiple GNU/Linux distributions available that will run on - and are in fact made for - older 32bit PC's (AntiX, Bodhi etc).

You should never run operating systems that have reach end of life, and as such do not recieve security updates in a timely order.

And I fail to see why an older kernel should work better than a new one, if it is non PAE you are looking for, there are alternatives (see above).

Please use the archive mirror provided by debian: http://archive.debian.org/debian/

The alternative is to use ISO DVDs, which can be found on their mirror so you do not need network during installation:

https://cdimage.debian.org/mirror/cdimage/archive/5.0.10/amd64/iso-dvd/

It seems your first problem from the questions and comments is using the netinstall image. It probably won't work nowadays.

For installing, the best course of action is using the full DVDs.

As for using something modern Debian based that supports 32 bits, you can use AntiX, as others recommended. However, it will be slower, as graphical environments nowadays expect more powerful machines.

I usually run the latest FreeBSD 32-bits on legacy hardware, have regular updates and much more satisfied with the resulting performance.