This is a significant difference, and should be easily detectable in a DNA test.

However, there are some possibilities that could cause you to share more DNA with a first cousin, such as having a double-first-cousin (where both of their parents are your parents’ siblings). I have some friends who married siblings, and this is their kids’ situation. Or the person could actually be your aunt (you also share 25% of your DNA with them) — I have an uncle who is only a couple of years older than me, and is more like a cousin.

There are probably some other, more exotic possibilities as well, that could result in sharing about 25% of your DNA with someone.