Basically Five runs around a bunch of corridors as in every episode before this one with him in it. This time though he's not doing it to save the world. He just wants to save Peri. Seriously, everyone fucking dies in this episode (even the silly armadillo monster and the bad guy who thinks he's on House Of Cards) except her, making her the first most important companion.
This of course begs the question of why the TARDIS brought them to Androzani Minor. Five does jack all except get himself killed and everyone on Androzani Minor was going to die either way. The only plausible explanation is that the TARDIS decided it was time for Five to regenerate and choke the life out of Peri, likely due to the TARDIS having sadistic fetishes for her.
The antidote to the spectrox poisoning was “milk from the queen bat,” so that means that the Doctor totally squeezed a bat's tit. This makes him the first sexual predator to appear on the show until Jimmy Savile.
Also we finally get an explanation as to why Five put a stick of celery on his lapel. That's cool I guess.
The Fifth Doctor heads to the planet Androzani Minor, which would later be referenced in the most canon and least coherent Christmas special of all time, when the Eleventh Doctor fends off a herd of Androzani tree harvesters.
Just don't think about it too hard.
Written by the omniscient Robert Holmes. Like most of Holmes' stories, he got the idea off of a /who/ audio mockup.