Fifth-dimensional characters are beings that cannot be perceived by three-dimensional beings (which is us). As such, throughout fiction, these characters take on another appearance, usually one familiar, that may hold the most emotional sway over them, so that they can be perceived.
An example of fifth-dimensional beings are the Contumelia (image below), from the Ben 10 franchise. Ben sees them as mascots of "Mr. Smoothy" (a restaurant that serves beverages) because he likes it very much. Other characters see Contumelia differently.

I will give an example:
• Bardock (TV Special/OVA) - Most likely one of his friends or Toma.
One defining trait of this Bardock gotta be his attachment to his close friends, which as far as we could tell, wasn't normal for Saiyans. The death of his friends was also one of the reasons he was able to trigger the Super Saiyan transformation. Bardock seems to hold them very dear, so it makes sense he would see them or at least Toma.
• Bardock (Dragon Ball Online/Dragon Ball Minus) - Most likely Gine or Goku.
Just like his counterpart, this Bardock seems particularly attached to the ones surrounding him, but in this case, it's his family. More specifically his "wife" and youngest son, Goku. It's also not a trait very common amongst Saiyans, which would set him apart from what Saiyans would probably and generally see those fifth-dimensional beings. Bardock holds his family very dear, so it makes sense he would see Gine or Goku.
Now it's your turn. Pick a Dragon Ball character, anyone, and imagine them standing in front of these extraordinary beings. Who or what do you think they would see and why? I will take the opportunity to ask: would you like to see fifth-dimensional characters in Dragon Ball or is it too much Western nonsense?