I took a mission to deliver some cargo two star systems away, when going into hyperdrive to get to the first star my speed went in the thousands * C , then I ran into a sun (I assume the star of which the title is named) . I readjusted for the second star jump and I'm going over 1kc its still 5 ly away and I've been at it for quite some time. Just curious as to whether this is just a normal quest which takes some time to complete, its strange that my target destination has maintained 5ly+ away and im going 1kc+ speed.
There are three different methods of traveling around the galaxy.
1) Thrusters - Normal Space (combat, docking at stations, flying into station walls)
2) Supercruise - Travel between planetary bodies and stations within a Solar System.
3) Hyperdrive - Travel between two different Solar Systems.
My assumption from your post is that you are going through systems A-->B-->C. You engaged your Hyperdrive to get from A-->B, and you're currently in B in Supercruise, trying to get to C. You just need to engage your Frame Shift Drive again (unless you have Hyperdrive set up to a separate key), and you'll do another jump.
Also to note: You cannot travel between two different star systems in Supercruise. You have to use the Hyperdrive.