“Why would they put a weapon with a 5,000 mile range in Mexico?”
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The same reason NATO would put a NATO nuclear missiles in Italy, Turkey and Germany. To attack their adversary.
We are at war with Russia, albeit mostly by proxy and that facade is fading quick. Missiles with a 5,000 mile range would be needed to hit Washington DC and the northern states of the USA. Assuming Yucatan Mexico Military base installation.
I'm pretty sure Russian ICBMs can reach the entire continental US from the Russian landmass already.
Most of us have lived through the cold-war. It was real.