how long would it take a space shuttle to travel to a planet 5 light years from Earth?

Too long.

9weeks

The Shuttle isn't designed for anything beyond Low Earth Orbit (plus, the entire fleet has been decomissioned).

But think about it this way.  Voyager I has the fastest 'relative to the Sun' velocity we have acheived, at around 17 km/s.   We needed the use of a gravitational slingshot (gravity assist) around Jupiter AND Saturn.  At this rate, Voyager I will reach one light year in over 17,600 years.  Multiply by five for a ballpark estimate of a little under 100,000 years to travel five light years, best case scenario.  That assumes, of course, that you can make use of the multiple gravity assists.  If multiple gas giants aren't in the right parts of their orbits, it can't feasibly be done.

You could shave a few years off the total voyage by spending more money on fuel, but the cost to rewards ratio tapers off when you do this, as adding more fuel also means adding more mass, which requires more force to accelerate to escape velocity.

The Autobots will not have problem traveling there.

Assuming that the space shuttle were to travel at 17,000 miles per hour, the time at which it would take it to travel 600 light years or 3.6 quadrillion miles would be 2.1x10^11 hours or 8.8 billion days or 24 million years.

Well, Distance = rate*time. We have our distance (600 light years), and we're asking for time, so we need a rate. Depending on your proportion system it could take a few seconds or hundreds of billions of years. My personal favorite is the Infinite Improbability Drive used in Hitchhiker's Guide to the Galaxy. In which reaching your destination (any destination) is all a matter of how quickly you can find how improbable it is that you just appear there at random.

It will take our  best space shuttle about 220 years to get there to Kepler. Our best chance is the use of our android robots. they are lighter and travel faster in space. I am 30 years old so nothing that we send now will land on that planet until after I am dead and gone but our children will be the ones to benefit from the work that we do now. Our children are the next and new space cowboys of the future.

well, if i was on the shuttle and i ate tacos rite before lift off. i would need to find a bathroom about 5 hours into the trip. so i would then take over the controls and go balls to the wall. according to my calculations it would take me about 7.3984 hours to reach Kepler 22b. plus or minus .5 hours for toll booths. then i would be the first person to poo in the woods there.