Doesn't seem like you are asking a question. Obviously litigation is costly and can be expensive. You should consult with a copyright litigator to closely review your case, facts and provide an assessment.
"Having the copyrights" is key, but it is not clear what you mean by that. If you mean your beats were registered in the U.S. Copyright office, you may be in a position to recover both infringement damages and attorneys' fees. Nonetheless, there may be defenses they may wish to exploit, for example you "did not think it was a huge deal at the time," so they may argue you acquiesced, or tacitly agreed or that it would be inequitable for you now to pursue the claims. You should consult a copyright lawyer.
You wrote that: "Roughly 5 years ago a well known artist used 10 of my beats for online releases without my consent or any agreement being made."
Five years ago you KNEW a "well known artist" copied and published your music and yet you chose not do anything about it. Why do you think you can do something about it now? Have your own copyright attorney review the matter but my take is that the well known artist can easily defend the case by asserting that you've sat on your rights [the "laches" defense]. This likelihood precludes, in my opinion, the possibility that an attorney will take your case on contingency.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.