What size and how full are the two partitions on the 320GB drive?
There are numerous ways you can do this. Unless you have other backups located elsewhere (and you should!), they all involve at least a little risk.
This is very general - consult the guide for specifics depending on what strategy you choose.
1) Since you have a brand new 500GB drive I'm assuming it's not even close to full yet. Copy everything from the 320GB drive to it, then delete both partitions on the 320GB and make just one new one. This will only take you about five minutes longer than whatever amount of time the data-copying process requires.
2) (This leaves the 500GB drive clear out of the picture. If your main data storage is there it probably makes sense to not mess around with it right now unless you have to. The most critical time when re-doing a backup plan is if you get in the situation where you have to temporarily delete all your backups, like may be the case in Case 1 shown above.)
Look at the two partitions on the 320GB drive, pick the one with the most free space, then move as much of the data from the other partition to the free space as you can. If it will all fit in one shot, delete the empty partition and extend the one that now has all the data. If it won't all fit, keep going.
For example, if it's like this:
Partition 1: 160GB total; 80GB used / 80GB free
Partition 2: 160GB total; 110GB used / 50GB free
I would move about 40GB from Partition 1 to Partition 2, leaving you with this:
Partition 1: 160GB total; 40GB used / 120GB free
Partition 2: 160GB total; 150GB used / 10GB free
At that point, shrink Partition 1 down to about 60GB. At that point what you'll have is a drive that looks like this:
Partition 1: 60GB total; 40GB used / 20GB free
100GB FREE SPACE - Unallocated
Partition 2: 160GB total; 150GB used / 10GB free
Then extend Partition 2 by the 100GB of Free Space in the Unallocated area. Now you've got this:
Partition 1: 60GB total; 40GB used / 20GB free
Partition 2: 260GB total; 150GB used / 110GB free
Then move the remaining 40GB of data from Partition 1 to Partition 2. Now you'll have:
Partition 1: 60GB total; 0GB used / 60GB free
Partition 2: 260GB total; 190GB used / 70GB free
Since Partition 1 is now empty you can delete it and extend Partition 2 to encompass the entire drive.
Obviously, your exact numbers are likely to be different. This ought to give you the idea, though.
One thing I'd recommend is to not be tempted to shrink a partition down to the point where there is little or no free space - give the program a little elbow room to move data around.