You're getting answers about the asteroid belt because you said asteroids, but I believe your question is about the Oort cloud (comets) since you said surrounding the solar system.
From wikipedia;
> Space probes have yet to reach the area of the Oort cloud. Voyager 1, the fastest[60] and farthest[61][62] of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years[6][63] and would take about 30,000 years to pass through it.
From wikipedia;
> Space probes have yet to reach the area of the Oort cloud. Voyager 1, the fastest[60] and farthest[61][62] of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years[6][63] and would take about 30,000 years to pass through it.