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