I installed Win7 as a dual boot with Ubuntu 14.04 "Just in case" I ever needed a Windows program that just couldn't be emulated, but I haven't really run into the problem yet. Instead, I'd like to take all of /dev/sb1 (or at a minimum the free space of it) and add it to /dev/sdb5. Is that possible to do without problems, and if so what is the best way to go about it?
I'm guessing the /dev/sda1 is where your windows installation is - you might be able to shrink that partition some, but that operation should be done while windows is running, using the windows disk manager. Make a backup first!
Then, using a live CD or live USB, you will need to add gparted to the usb while in the 'Try Ubuntu mode'
sudo apt-get install gparted
Then, you can run gparted against the disk, and move or resize the remaining partitions.
It's possible to delete or resize your /dev/sda1 and then adjust the size of /dev/sda4 and /dev/sda5 to cover the freed space; however, that will involve moving the start point of your root (/) filesystem, which is always a bit risky. You'll also need to do this from GParted on a Linux emergency disk.
IMHO, a better solution, if you're willing to completely wipe everything on /dev/sda1, is to repurpose that space as a Linux /home partition. This process is described in Move home folder to second drive (see especially Takkat's response), and I'm sure in other questions/answers on this site. This procedure poses less risk to your root (/) filesystem. In your case it will leave root (/) a bit on the large side, but not ridiculously so. Given the amount of disk space you seem to be using, it looks like you'll have plenty of space for storing your personal files.
You can use a live .iso version of gparted, and pass along the space from one partition to its adjacent counterpart. See the instructions in the first post here, and dismiss the dogma of the posters saying you should re-install:
