Dragon Ball is probably best known for its fight scenes and dramatic power boosts, which usually result in a new form for a fighter. The Super Saiyan Form is the most famous to come out of the series, notorious for its levels of escalating power. Since the transformation's debut in Dragon Ball Z, there have been multiple levels introduced.
The levels of Super Saiyan vary in usefulness and usage, but all get their time in the sun -- even the currently-not-canon Super Saiyan 4. But one that has been mentioned but never explored in the canon universe is Super Saiyan 5.
The first time SSJ5 was brought up was in Dragon Ball GT, during a discussion between Vegeta and Bulma. While GT is no longer canon, one thing that fans still hold onto from the series is the idea of Super Saiyan 5. In the episode, Bulma is working on a "Blutz Wave Generator" that she hopes will help Vegeta produce the energy needed to reach Super Saiyan 4. She goes on to say that it will help him produce so much energy that he "might even reach Super Saiyan 5." Although Bulma's just joking, Vegeta notes that Super Saiyan 5 could be possible.
Ever since then, fans have speculated whether the form is indeed actually achievable. In 2000, rumors were spread all around the internet about the supposed new series, Dragon Ball AF. The rumors got fans excited again, and to this day, many are still waiting for Toriyama to unveil an official version. However, it seems that he isn't interested in exploring the idea. In Twel-Buu Mysteries, a special Q&A project published by Saikyo Jump in 2014, Toriyama states that "After the fight with Beerus, Goku realized that mastering his normal state and Super Saiyan would raise his level more and sap less strength, so I think he probably won’t become Super Saiyan 2 or 3 anymore." Super Saiyan 5 is also hindered by the fact that Toriyama didn't write for Dragon Ball GT the way he is for Super currently, so even Super Saiyan 4 isn't canon anymore.
But, despite its "could've been" status, it's still fun to imagine what Super Saiyan 5 would be like. Were a Saiyan to achieve the form, it could look like any combination of previous Super Saiyans. The general consensus among fans seems to be that it would include the ape-like appearance of Super Saiyan 4, but with an altered color pallet. The Saiyan's hair would grow longer and muscles would grow bigger, as usual, but the color of the hair and fur would be the same, maybe gold or silver. Proponents of the idea seem to agree that the hair would grow to the length of Super Saiyan 3, the previous canon transformation.
It's also likely that to generate the energy needed to reach Super Saiyan 5, the user would need to be able to use God Ki. This would mean that, instead of a cross between 3 and 4, 5 would be a cross between 4 and God. Because both SSJ4 and Saiyan God isn't part of the linear path of the original Super Saiyan form, they could possibly be stacked. In this form, the energy output would be tremendous and most likely boost the user's attacks to a degree never seen before -- maybe even to a world-ending degree, much like Frieza's Earth Breaker attack. And, of course, the form would come with a physical power boost.
However, there would definitely be major side effects of using so much energy. In addition to this, there are time limits to both the Super Saiyan 4 and Super Saiyan God forms. Combining them would most likely result in a shorter time limit for a combination form, though a form like Super Saiyan 5 would likely be tough to maintain even without being a combo form. It's possible that in order to maintain the form for any extended amount of time, the user would need to drain the energy of those around them, whether consciously or unconsciously. Generating enough energy for the Spirit Bomb takes many people giving their energy to one person, so it's possible that a higher Super Saiyan form could require something similar.
Only time will tell whether Toriyama eventually answers fans' call for Super Saiyan 5. But, to do so, he'd need to work around the elephant in the room that is GT and Super Saiyan 4. Despite no clear version in canon, fans all across the internet have filled in the gaps left by a simple line in what Toriyama calls a side story.