Warning: Spoilers of Series 5 lie ahead, please do not enter without authorisation.
Director of Series 1-4 Ed Bye left before 5. Newcomer Juliet May was brought on board the Dwarf, but left after four episodes as it was too demanding for her. She was about right; from this point onwards, the stories started to become more complex.
Two changes were made to the characters, both costume-wise. Rimmer started wearing a red suit, possibly because of the success of Camille's hologram suit in Series 4, and a slimmer, more sophisticated 'H'. Kryten's head had more angles carved into it, and it looked somewhat flatter, more oblate. Rimmer also became solid for half of this series, in one way or another. He was made permanently solid later on.
"Holoship", another love story aired near Valentine's Day, saw Rimmer being given the chance to join a crew full of super-intelligent holograms... and falling in love with one. Apparently Jane Horrocks (Nirvanah Crane) based her character on Joanna Lumley's character in Absolutely Fabulous.
"The Inquisitor" is a simulant with a very advanced gauntlet. He judges each human being and exterminates those who don't appreciate the gift of life. Needless to say, the Dwarfers are in trouble...
Rimmer and Kryten go moon-hopping in "Terrorform", and they come across a moon that changes shape into a metaphor of Rimmer's mind. Unfortunately, it has kidnapped Rimmer. The classic scene in this episode was Lister and the Cat at the computer talking about the 'taranshula'.
In "Quarantine", the crew explore a viral research centre, but leave Rimmer behind on Red Dwarf. Concerned that he will contract a hologrammatic virus, Rimmer sticks the others into quarantine for 3 months. This was the episode in which Rimmer was first given access to the Space Corps directives, which Kryten had been constantly using against him. It was probably a bad move, as Rimmer would misquote them in the next few series.
"Demons and Angels" roam the Red Dwarf universe as the crew makes two sets of identical copies of themselves... identical, except for one minor detail: one set is spiritual and divine, and the other is "fish bait". Check out Low Holly's costume: since she was wearing a black wig, the background and poloneck had to be changed also.
The crew are brought "Back To Reality" after crashing undersea. Nobody is as they were on Red Dwarf: the Cat has become Duane Dibbley, a man who plays with a yo-yo; Kryten becomes Jake Bullet, a detective in charge of traffic control; and Rimmer and Lister are half-brothers, Rimmer a tramp and Lister a successful businessman.
So that's it for Series 5. Click here for Series 6... or here if you missed something from 4.