The Five Towns eruv is contiguous to the Far Rockaway eruv, so I'll assume that the Techum of Far Rockaway extends through the Five Towns. The shortest straight-line distance between the closest points of the borders of the Five Towns and West Hempstead eruvim is, according to Google, almost exactly 3km or 9700 feet. Techum Shabbos is 2000 amot, which is approximately 1km, thus placing West Hempstead significantly past the techum.
However, according to the Orthodox Union,
The techum starts at the last structure in the city and the size of the city makes no difference. (A city is either enclosed or the buildings are within 70 cubits of one another.) If you live in New York City, you can walk freely from Battery Park to Harlem.
According to this, you would be able to freely walk from Far Rockaway well into Suffolk County before leaving the techum.
Disclaimer: I'm not an expert of eruvin or techum shabbos, and I may be going about this all wrong. CYLOR.
Its not as simple as Shmuel makes it sound. From Far Rockaway to West Hempstead you have to pass over at least three major highways (I878, Sunrise Highway, and The Southern State Parkway). All are significantly wider that 70 cubits. Water features (lakes and rivers) also complicate matters.
There is an additional halacha that when 6 houses are within 70 of each other, to join with another group of 6 houses, the distance between them can be up to 140 amos (roughly between 210 to 280 feet). This can get us over the 878 and possibly the Southern State, but Sunrise Highway with the LIRR tracks is even wider that this.
A Techum is established by a) figureing out what the halachic dimentions of the city is (which houses are close enough together) B) in most cases "squareing the city" drawing a north-south line at the eastmost and westmost points in the city and a east-west line at the northern and southern ends of the city. The Techum is 2000 amos from the lines drawn. It is possible that the squaring of the city could bring west hempstead in to the techum, I dont have the time or expertise to even try to do somthing like this, even from google maps. CYLOR
As an aside, even with the larger 140 amah techum, there is no way that the "city" could include anything east of the Meadowbrook Expwy, far short of whats required to get to Suffolk County. (Squaring wont help, as the Meadowbrook runs from shore to shore.
There are Poskim who claim that every thing included in one eruv can be considered one city, (used in Jerusalem to allow walking between Har Nof, Ramot, Ramat Shlomo and the city center).
In short, not simple at all, dont do it without CYLOR, and probably not allowed