I hate my mom's lack of responsibility for her pet
Oh no. What is going on with your mom and her pet?
I don't want to clean up after that damn animal, who has been living here for around 5 years
When someone adopts a pet its expected that they take care and clean up after it. It's not unreasonable to be upset at someone who doesn't. If you don't talk to them about this you'll just continue to resent them.
Fine I'll talk to them after I'm done doing it.
That's a good first step. Try to remember to be patient and calm, as she may not be too aware that she is neglecting her pet. Try to make sure you teach her some of the things that she needs to do so that her pet will continue to be healthy instead of being neglected.