Dell Precision T1650 GPU and PSU upgrade possible?

Hello,

 I have a Dell Precision T1650 Workstation at my school that I use for deep learning. I was wondering if I will be able to swap the original L275AM-00 PSU with corsair RM550X and add GTX1070? If the GPU is too long I can just get rid of the drive bay. Here are the system specs: 

Intel(R) Core(TM)-i5-3550 CPU @ 3.30GHz (4CPUs)

4GB RAM

0X9M3X Motherboard

I'll be using the GPU mostly for Deep Learning calculations.

Any suggestions and replies regarding T1650 and GPU recommendations are welcome.