My mentor is advising me to "not worry about the cost"? In my school,  we have a program that allows students to do research as an undergrad with a mentor.  Not uncommon. Naturally,  as a participant,  this is my first dive into the world of research.
I am choosing to do research on high power lasers.

The school gives us a 3 figure budget,  but when my mentor heard of the laser being 5 figures, she told me "don't worry about it." And mentioned that she has something, but i didn't quite hear what she said. She kept putting emphasis on keeping on going "don't let the cost stop you", etc.

Is this common?  Should i apply for a grant? I'm not sure anything 5 figures is worth undergrad research. Is this generally the case?
Your mentor, or prospective mentor, is telling you not to worry about the cost. Presumably, they know what they are talking about and have funding that can cover the costs. A $50,000, I am assuming US, laser could be easily covered by a large NSF/NIH type grant or start up funds. If it is a piece of equipment that the mentor needs for their lab and will use in the future, then it is no big deal. You are not taking money out of anyone's pocket. That said, you should realize that you will not be able to keep the laser at the end and it will likely stay in your mentor's lab.