Are there any Baryons that have quark-antiquark combinations? I'll be honest, I only have a Highschool education, so there might be something obvious I'm overlooking. However particle physics is of massive Interest to me. 
My question is, I know there are unstable quark-antiquark pairs that form Mesons, but are there any Baryons that are not wholly made up of quarks or antiquarks? i.e. "up, up, anti-down"
If the answer is no, why not? 
 A: Yes, there are some oddball baryons that contain four quarks and one anti-quark. They're called pentaquarks. These could be thought of as a baryon with three quarks plus a meson with a quark anti-quark pair, but sticking to each other more than they should. There are few hadrons that survive more than a tiny fraction of a second, and only the proton and neutron live longer than one second. The "sticky" baryon-meson combinations are found through analysis of scattering data at the major particle accelerators.
The known pentaquarks are: $P_c(4450)^+$, $P_c(4380)^+$ ([CERN 2015][1], [Arxiv paper][2])  and $P_c(4312)^+$ ([CERN 2019][3]) - oh but wait, the 4450 one seems to really be two pentquark peaks close together in mass - 4440 and 4457.[CERN][4]   BTW, the subscript 'c' indicates that one of the constituent quarks is a c (charmed) quark.
There's a tetraquark - two quarks and two anti-quarks in one bag - with mass 4430, named $Z(4430)^+$ (nothing to do with the Z boson). [CERN][5]   Can it be described as two mesons being "sticky" with each other or is it better described as a more tightly-knit group of four of the little buggers?
Another possible exotic hadron is made of six quarks all stuck together. This is a "dibaryon".  When I was an undergrad in physics, I worked with Dr. Yokosawa at Argonne National Laboratory on finding bumps in polarized proton-proton scattering. That was an interesting experience.  As of last time I checked the literature, there was [only one found][6] that stood up to analysis, but always there are candidates due to unexplained wiggles in cross-section vs energy plots. These usually turn out to be something less exotic. Interesting, but since anti-quarks aren't involved, never mind!
[1]: https://home.cern/news/press-release/cern/cerns-lhcb-experiment-reports-observation-exotic-pentaquark-particles CERN’s LHCb experiment reports observation of exotic pentaquark particles (14 JULY, 2015)
[2]: https://arxiv.org/abs/1507.03414  Observation of J/ψp resonances consistent with pentaquark states in Λ0b→J/ψK−p decays (LHCb collaboration)
[3]: https://home.cern/news/news/physics/lhcb-experiment-discovers-new-pentaquark LHCb experiment discovers a new pentaquark
[4]: http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html#Pentaq  26 March 2019: Observation of new pentaquarks
[5]: http://lhcb-public.web.cern.ch/lhcb-public/Welcome.html#Z%284430%29 9 April 2014: Unambiguous observation of an exotic particle which cannot be classified within the traditional quark model.
[6]: https://arxiv.org/abs/1610.05591 On the History of Dibaryons and their Final Observation, H. Clement
A: No, a three-quark baryon can not be be made out of two quarks and one anti-quark (and vice versa) as this would necessarily give the particle color.
Each quark carries one of three colors (red, blue, green) and each anti-quark respectively carries anti-color. Color is an additive quantity when constructing particle and the result must be color-neutral, i.e. it either is made out of for example red + anti-red or red + blue + green quarks. Although we can not observe the "color" of the constituents of a particle directly (as all observable particles must be color-neutral), we can measure its effects indirectly via certain cross-sections.
With this being said, we can now clearly see that there is no way in which we can construct particles of two-quarks and one anti-quark as any possible combination would not be color-neutral. Hence, color-neutrality forbids observable three-quark particles composed out of quarks and anti-quarks.
Penta-quarks however can and must contain quarks and anti-quarks as mentioned in a previous answer.
A: Pentaquarks contain three quarks and a quark-antiquark pair, and they are baryons, since baryons are defined as having an odd number of valence quarks.
