I'm asking and answering my own question to find the answer later (and to help anyone stuck using the ancient Borland C++ 5.02 compiler for some reason).
I have Borland C++ 5.02 installed in a 32-bit Windows XP virtual machine, with a BC++ project residing in a folder shared with the host computer (mapped to drive letter H: in the VM). The project compiles successfully, but always fails the final step with this message:
Could not load: tlink.exe
My compiler is installed in the usual C:\BC5 location in the virtual machine, but it turns out that it can't handle project folders on paths that contain spaces in their names. So I copied the project from that shared H: drive to C:\BC5\[project] and voilà! it compiles and links with no problem. I've also copied the project folder to my virtual machine's root C:\ and that works as well.