WHETHER UPANAYANAM CAN BE PERFORMED AT THE AGE OF FIVE?

We have to always keep in mind that in respect of any karma, dharma SAstras provide for multiple options .

According to Manu, a BrAhmaNa who is desirous of brahmavarcas can be performed Upanayanam at the age of five.

brahmavarcasa kAmasya kAryam viprasya pancame !
--- Manu

According to Angiras, a BrAhmaNa who is desirous of brahmaVarcas can be performed Upanayanam at the age of five.

brahmavarcasa kAmasya pancame abde agrajanmanah !!

--- Angiras

WHAT IS THE MAIN PURPOSE OF VEDANGA JYOTISHA?

Vedas are intended for the performance of yajnas.

VedAnga Jyotisha is also known as KAla vidhAna SAstram as understanding time is necessary for performance of yajnAs.

vedA hi yajnArtham abhipravruttAh
kAlAnupUrvyA vihitAsca yajnAh !
tasmAd idam kAlavidhAna SAstram
Yo jyotisham veda sa veda yajnAn !!