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
• start gparted
• 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