Because you're using a MBR partition table, and using extended partitions, resizing can be a little bit tricky, but here we go...
Note: If you have good backups, you may just wish to wipe the disk and reinstall Ubuntu fresh
Note: You don't want to add space to sdb3, but rather sdb6 and sdb7.
Make sure that you have a good backup of your important Ubuntu files, as this procedure can corrupt or lose data.
Keep these things in mind:
always start the entire procedure with issuing a swapoff on any mounted swap partitions, and end the entire procedure with issuing a swapon on that same swap partition
a move is done by pointing the mouse pointer at the center of a partition and dragging it left/right with the hand cursor
a resize is done by dragging the left/right side of a partition to the left/right with the directional arrow cursor
if any partition can't be moved/resized graphically, you may have to manually enter the specific required numeric data (don't do this unless I instruct you to)
you begin any move/resize by right-clicking on the partition in the lower pane of the main window, and selecting the desired action from the popup menu, then finishing that action in the new move/resize window
Do the following...
Note: if the procedure doesn't work exactly as I outline, STOP immediately and DO NOT continue.
- boot to a Ubuntu Live DVD/USB, in “Try Ubuntu” mode
- remember your swapoff command for /dev/sdb5
- right-click on /dev/sdb3 in the lower pane and select move
- move /dev/sdb3 partition all the way left
- if this gives you trouble, stop here, let me know, and we'll do it another way
- resize the right side of /dev/sdb3 all the way right
- resize the right side of /dev/sdb7 right to add ~70G to /home
- move /dev/sdb7 partition all the way right
- resize the right side of /dev/sdb6 all the way right, adding ~15G to /
- click the Apply icon