In 1985, they did have mainframes at the Pentagon. But they dated from the 1960s.
My first job out of college in 1989 was to go to work in the basement of The Pentagon for the Defense Communications Agency, as an Analyst/Terminal Operator for those old pre-Multics Honeywell WWMCCS mainframes. One of my first jobs there was to help modernized the classified Airfields database from COBOL 66 to COBOL 77.
At the beginning, we used glass tty terminals that were wrapped in faraday cages, and all local printing was done via a screen print function to local thermal paper printers. We could use the line printers, but those were not directly accessible to us, and we had to go up to the Operator window to ask for our output.
They later upgraded the terminals to EMF-hardened IBM PC XT computers with removable 5GB hard drives, known as WIS-CUC terminals. That was like 1991. Note that this was PC XT technology from like 1984, not PC AT.
The unclassified PC AT type computers we used outside of the classified environments probably had more RAM, larger hard drives, and more I/O capacity than those ancient Honeywell mainframes.
So, no, there weren’t any supercomputers at the Pentagon in 1985.
Now, if you want to talk about NSA headquarters at Fort Meade, then that’s a different story.