All limited expresses in Japan have their own distinguished name.
Tokaido shinkansen uses Nozomi, Hikari and Kodama. Kodama is a train which calls at all stations. On the other hand, Nozomi and Hikari do not stop at all stations. Nozomi calls at only major stations which cities are over one million population.
Azusa is a limited express which connects the nation capital and Matsumoto city in Nagano prefecture(some trains continue to Hakuba or Minami-Kotari). Matsumoto is not a prefecture capital nor million inhabitants, and the cities along the Chuo Main line is not so big as you compare to Tokaido main line. However, there are many tourists using the limited express, and also hikers who are going to the mountains. Azusa departs each hourly between Tokyo's Shinjuku station and its composition is 11-12 cars, which is quite long for daytime trains with high frequency.
Duo of brothers, Karyudo sang a song called Azusa nigo. Nigo means number 2. The song 's lyric says that Azusa No.2 departs at 08:00 and heads to Matsumoto. However, JR(or even then JNR) uses even number for inbound train to Tokyo! Which means than Azusa heading to Matsumoto should be odd number as like Azusa no.1 or Azusa no.2. Current Azusa no.2 departs Matsumoto at 06:08.
Train leaving Shinjuku at 08:00 is not Super Azusa no.5. Prefix Super means that the train is faster and usually newer than without Super.