In four-part writing, you would normally double the root.
True, but "normally" doesn't mean always. It's a preference, and voice leading considerations typically override that preference for any given chord.
In five part writing, the order of preference is the same, but you have additional considerations of balance. If the root is already doubled, you might want to double the fifth rather than the root.
In five part writing, the reasons for the preferences are also the same. For example, a major third will often tend to resolve up by half step (for example, in a perfect cadence), and doubling the major third can therefore lead to odd voice leading in the part that doesn't follow the tendency. That principle pertains regardless of the number of parts.
Another reason for avoiding doubling the third is that the tuning of the root and fifth of a chord are less likely to be controversial between two players or two sections. There's not as much leeway for the root or fifth to be sharp or flat without sounding bad, but opinions on the proper place for a third can vary by 20 cents or more (the difference between an acoustically pure major third and a Pythagorean major third is 21.5 cents).
That said, I was looking just yesterday at a Handel chorus in five parts that begins with the tenors and first sopranos doubling the third. That's a B-flat major chord. The next chord is an F-major chord, and the first sopranos have the fifth on C, while the tenors have moved to the third on A. The "odd" voice leading there is for the tenors, of course, but it's not particularly odd.
So any rules about doubling any given chord tone are subordinate to voice leading considerations, especially to the prohibition on parallel unisons, fifths, and octaves.