So, time has gotten away from me. I had the strings and cables replaced on an old Mathews bow "a couple of years ago," fully intending to get back into shooting.

Haven't drawn that bow more than a dozen times since then, and that was shortly after the replacements.

Just found the receipt. Dated 2014!

Stored indoors in controlled climate, strapped in it's hard case.

Do ya think I need new strings?

Nope - go sight it in and hunt with it.

Shoot it.

Bought my Mathews and had the string on it for 15-years. Still shot well, no broken strands. I just decided to replace it on principle but there was no real need to.

If there is a doubt, prudent move is to replace them.
It is impossible to see under serving....

Was poking around in the closet and found the Mathews booklet that came with my bow. It said to replace the string and cable every 2-years. Really?? 15-years may be too long but 2-years is just crazy.

Its fine, just check the axel to axel length

Depends on how it was stored, how much it was shot, and if damaged (like abrasion walking through CRP).
Some folks need one every yr, some folks can go years.

Mathews factory strings are a crap shoot. Some sets tend to stretch a lot and in a short time. Some dont budge even after thousands of arrows. If your strings arent damaged in any way, just make sure the bow still makes its stamped peak weight and the draw length is correct. If either is out of spec have your local shop get it back into specs and go shoot. Very little wax on string material only will keep them in good shape. Do NOT wax the serving. If you dont have a shop you trust, shoot me a pm. Im back tuning bows again and several members here can vouch for my work