Is my transmition going bad ?
 

Hey guys, I feel like my car is taking a little extra time going into 5th as it stays in 4 for quite the length of time.

Last night I took my wife out in it for the first time and was going a little fast each time I was at the stop lights. Well I took a right turn and sped up to get into traffic and it reved up hard in 4th and was loud and never went into 5th for the longest time and was really loud.

Is it also bad for the car to be wizzing first off the lights even in my 2.5 auto?

it depends on how you drive it. the transmission will adapt to the current mode of driving. if you're mashing the pedal, it'll wait until close to redline before switching gears, additionally, it'll avoid shifting to the next higher gear on hard turns and overtakes. this is all normal.

if however, you don't think you were driving particularly hard (holding the pedal down past kick down) and driving more docile and it's still waiting to change, it could be something more.

first, you don't mention how many miles you have, if you were in manual or automatic mode or if it was displaying any faults / lights.

it may be time to change the ATF. it could be a vacuum line or a sensor.

get a durametric or have someone check for codes / problems.