We don't lack the industrial capacity either, we mostly lack a good reason to spend these resources in that direction.
And IMHO that's the main explanation for the Fermi paradox: we don't see aliens everywhere because they don't have a good reason to colonize other planets than their own either.
We do lack the technological capacity.
Travelling to another star would require a fully self-contained spaceship with energy, life support, food, medical facilities, even production facilities able to function for centuries or millenia. We simply don't know how to do that.
Pure race long term survival, any sane civilization knows very well a single space item hurling fast enough can wipe out all conplex life on planet. Or vulcanoes, tectonics etc. Also every star eventually goes down, usually pretty violently (but thats properly a long term concern).
Its not 'if' question, just 'when'. You cant be space faring civilization and not know this.
Once it becomes cheap enough then religious or similar cults will do it, and the cost of doing isn't a great deal more than colonising the solar system where are are economic benefits.
That assumes reaching 5 light years in say 50 years
However once it's done a few times, then it can't be stopped. If you're going at say 1/1000th of the speed of light (50 years to travel, 450 years to settle and build the next wave is 1% the speed of light) then your successor species will have colonised the galaxy in 100 million years, and we know that hasn't happened.
Would that not also imply that improvements in ease of access to space, increase of energy production and -price reduction all level off before it becomes easy and affordable enough that mere curiosity would suffice to make it possible, for ALL civilizations?