It means a little bit more than that. Mach 5 at sea level is usually when the properties of air changes into a plasma. The electrons are separated from their atoms creating an electrically charged plasma that the vehicle travels through. The speed where hypersonic is defined differs at higher altitude due to the composition of the fluid it travels through. I’ll have to dig up some old textbooks to get a more accurate definition though.

Source: Aerospace engineer who worked on hypersonic projects for the Air Force

EDIT: The conventional rule of thumb is to define hypersonic aerodynamics as those flows where the Mach number is greater than 5 however that is no more than a rule of thumb. Hypersonic flow is best defined where certain physical phenomena become progressively more important as the Mach number is increased. In some cases these phenomena might become important above Mach 3, in other cases they are important above Mach 7. Example phenomena:

• Thin shock layers
• Entropy Layer: It’s a region of strong vorticity and effects boundary layer calculations
• Viscous Interaction
• High Temperature flows
• Low-Density flow

I forgot to mention before the edit that the actual shape of the object traveling through the fluid also effects when the fluid becomes hypersonic due to it’s interaction on the fluid (shocks, recapitulation, boundary layer interactions, etc.).

Source: Hypersonic and High-Temperature Gas Dynamics 2nd Ed. (John D. Anderson Jr.)