There you were holding the baby, chatting on the phone, all is right with the world - yeah, not so much for your 5 year old.
Biting the baby is really wrong and your 5 year old is old enough to understand that. Time out never worked with my son - he would sit in a corner and amuse himself - sing songs, play with imaginary - I think he actually liked it. So, I took away privileges - favorite toys, his already limited TV time, etc.
Talk to your oldest and, once again, explain the rules regarding the baby, then explain the consequences for breaking the rules. Make them count. and stick to your plan.
Also, I am sure you do, but engage your oldest in helping you help the baby - she could bring you a diaper, pick out an outfit for the baby to wear - little things that will engage her with the baby. Make sure you do spend one on one time with your oldest.
Biggest thing - you must stay calm - when you react you are giving your oldest attention - albeit negative attention - but sometimes that just feeds the bad behavior.
I think we expect them to be as joyous with the new addition as the adults are - but let's face it - those new babies just rock their little worlds. Heck I still tease my older sister about the family stories - seems she tried to give me away for the first 2 1/2 years of my life before she realized my parents were firm on keeping me.
Good Luck
God Bless