If you can run one mile in 5:30 then are you guaranteed to be able to extend that pace to 5k, 10k, half marathon, or marathon distance? Ignoring time needed for exercising and building up for the distance.
No. If your fastest pace for 1 mile is 5.30. Unfortunately the further you go the pace will drop off. There's various websites that will predict your race times based on other distances, ie I guess it works out your potential. Here's one http://www.coolrunning.com/engine/4/4_1/96.shtml
You can help reduce the drop of pace by interval training and a long run a week, but you can't stop it
First things first, it is possible, though not guaranteed. I did it for my 5KM and 10KM pace, not half and marathon. It comes down to training, and this is a lot of hard training.
Lets start off - a 5:30 mile is a strong pace, compare to your average runner, that is 3:25KMs or 17.56KM/h (10.9Miles/h).
I managed to build my pace over two years. When I started my 1 mile was close to yours, in November my 5 and 10KM pace was faster then my old 1 Mile pace. This was more an accident than a destination.
My journey started by going longer distances. By the time I did a few half marathons and marathons, a 5KM was very simple. I wanted to improve my half and full marathons pace. As such I used the 5KM and 10KM as chances to go hard. I would set the treadmill as high as possible and just go for as far as I could go. This translated to much faster road running. My half and marathon times dramatically improved but no-where near what my 5KM speed is.
Ultimately a 5:30 mile is a good pace to keep for a half marathon-even a 10KM. It would put you in the top 5% for big fun runs.
I say train really hard and eat clean.