As we all know that baryons are made up of three quarks while mesons are made up of a quark and an anti-quark. Is it possible for a particle to exist with five or seven quarks? Can a particle exist consisting of three quarks with color quantum no. (red,green and blue) and a quark and an anti-quark with opposite color quantum no. I am not sure if such a system will qualify for a pentaquark system.
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Mesons and Baryons are the most common objects quarks make.
However, they are not the only ones.
There are tetraquarks (=4 quarks, in the form $qq\bar{q}{\bar{q}}$, due to color confinement), such as the Z(4430) confirmed by LHCb with a significance of 13.9$\sigma$, see this for relevant references.
The treatment of these objects theoretically is more difficult, and as they contain more quarks, they are generally with higher rest mass.
There are also proposed pentaquarks (=5 quarks, in the form $qqqq\bar{q}$, again, due to color confinement), and while two have been recently discovered in LHCb (See e.g. this), there are some who disagree (Not on the quark content, but rather on classification), see e.g. this.
For information about color confinement, see any QCD textbook, or these two (For a less detailed explanation):
About free quarks and confinement
http://pdg.web.cern.ch/pdg/cpep/color.html
So to summarize: Yes, such objects can exist, and we believe we have discovered a couple of them.
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1It might be helpful to clarify that a tetraquark is $qq\bar{q}\bar{q}$ and a pentaquark $qqqq\bar{q}$. – dmckee --- ex-moderator kitten Aug 27 '15 at 14:23
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@dmckee You're right, I've noted that, and added color confinement references. (Though since OP knows about mesons and baryons, he should know this) – Omry Aug 27 '15 at 14:30
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You might also interested in looking up for tetraquark
– Secret Aug 27 '15 at 13:14