Not being able to exceed light speed does not mean we can't get to other solar systems. As you approach light speed space and time contract. So, if you travel at around .88c for a year, from your perspective you will have moved .88ly in one year, but from Earth's perspective, double that in twice that time.
So, if you accelerate to .88c relative to Earth, then decelerate back into Earth's frame of reference, you will seem to have traveled 1.76ly in one year, even though from Earth's perspective, you have done it in two.
It is probably pretty reasonable to think Starfleet has sent deep space probes into other galaxies, but they'd still probably take awfully long to get there, and then years to send subspace communications back.