What makes water a liquid (when it is)?
Let me venture an answer as well as I can.

I would point out that the article you are referencing is speaking of the arrangement of molecules in bulk liquid water when it is talking about this "fifth water" being present. The key is to note that they say a "fifth water molecule in the first coordination shell (23)." That means they are looking at how water molecules are coordinated with each other in liquid water. They are studying a massive (compared to a single water) amount of water, so the question of its liquidity is no question at all.

The "fifth water" thing is curious because it is common belief that waters arrange themselves in a tetrahedral arrangement. This is known to be true for ice, but is in question for liquid water. For instance, this article about the liquid water hydrogen-bonding network indicates that water, as it is heated, begins participating in only two hydrogen bonds rather than four.

Now, to answer the question of what makes liquid water be liquid water (when it is indeed liquid water). I think from the outset, it should be clear that this is a very difficult question to answer and any answer will likely be debated. I say that because you must define how many molecules it takes to make a liquid which is a very difficult thing to do.

I will tell you, however, that I have some useful information from research I am doing on water clusters and eventually liquid water (as a computational chemistry research assistant). The largest cluster we have studied is called DD*(20,1) which means (distorted dodecahedron with a water inside the cluster).

An idea of what $\ce{(H2O)21}$ can look is this: (taken from this very interesting article) water 21 http://pubs.acs.org.ezproxy.spu.edu/appl/literatum/publisher/achs/journals/content/jpcbfk/2006/jpcbfk.2006.110.issue-38/jp056416m/production/images/medium/jp056416mf00001.gif

The DD*(20,1) arrangement is image C.

As you can see from these different isomers, they are very distinct and no doubt each monomer behaves dramatically different from the next monomer. 21 monomers is quite a lot for a cluster, but even this does not mimic the properties of liquid water at all particularly because one would still consider this a gas-phase cluster. The fact that we even have isomers is indicative of not being near the point where something is considered liquid water. There are water clusters whose energy minima have been identified theoretically all the way from n=2 to (I've seen an article that says) n=60. Read more about some of that here.

One point I would like to make is that in structure C, for the research I'm doing, we have identified the vibrational properties of many of the monomers as being significantly different from those of molecules in liquid water.

So, all that being said about water clusters, we are certain that many more than five or 21 waters must be present to truthfully call something a liquid. We should then start looking for a system which is just large enough to accurately predict the properties of liquid water which are found experimentally.

As it happens, it is very difficult to do this on any scale, theoretically, at least, and identifying how many water molecules one is dealing with during an experiment to a quantifiable amount of precision is quite difficult. There are, however, good approximations of liquid water which are generated using Molecular Dynamics simulation software (here's a wikipedia page about MD software). The various models used for approximating the behavior of water do quite well at mimicking water's properties from an MD perspective. You can read about the TIP4P model of water if you want.

From the paper I just linked about TIP4P, they say that they approximate the properties of liquid water using 360 water molecules in their MD simulations, so that can act as a reasonable baseline for how many monomers are necessary before a system behaves like liquid water.

I say baseline for an important reason. The results found in that paper use MD simulations which pull a clever trick. Rather than having 360 waters that essentially float around in a box with nothing at all beyond the edges of the box, the software will actually mirror the behavior of a molecule beyond the walls of the box in which you are simulating. That means if you pick a single water, you would find that exact same water in the same place a full "simulation box" away from where you originally found it. So, if this says 360 waters, the number of waters for which interactions are being calculated is actually much larger than the amount of interactions 360 waters alone would have.

All that leads me to conclude that water behaves like water probably somewhere around 500 monomers. It must be noted, however, that the monomers behaving like liquid water as we know it will be the monomers on the inside of those 500 (but likely more) waters. Once you get towards a boundary, things start getting weird.

Hope that helps.