I was recently watching a show that say we need at least 5 Higgs Boson to prove the existence of the dark matter because it will strengthen the concept of symmetry.
Why is that so? Because, I am not getting what it says.
The show you watched seems to get two concepts mixed up: Supersymmetry and Dark Matter.
The existence of Dark Matter is strongly hinted at by comsological and astrophysical considerations. It is the easiest explanation for several observations we make in the universe.
Supersymmetry on the other hand provides a candidate particle. The lightest supersymmetric particle is conjectured to be stable and could therefore constitute Dark Matter. Also, supersymmetry has (at least) 5 Higgs bosons, which is most surely the context in which that number came up in the show.
So, while the (direct) observation of Dark Matter and additional Higgs bosons at the LHC would make a strong case for supersymmetry, both concepts are primarily unrelated.