Can someone make sure if I'm doing this right? Am I able to solve for re somehow? Or can I just neglect it due to it being so small?

Also, I have no clue if I did the part where I have to calculate the peak voltage of the source and at the output? Am I doing this correctly?

Thanks again!

See figure(s) attached for problem statement as well as my attempt.

 

I would have assumed re≈25/Ie(mA)=25/.25=100Ω.

This would mean with vbe=10mV that ie=100uA meaning vsig=1100*100uA=110mV

With a gain of 5000/1100=4.545

this gives vo=500mV