Hi Maiahsdad !
the only way to delete unwanted album from your iphone5 is to delete all the photos and remove the unwanted album from the pictures folder in your computer and Sys them to your iphone !
how do you delete all the photos ?
open Itune in your computer
in the left side you will see
DEVICE : in this folder you will see your computer name : click on it , then look in the right side you see
Summary__info__App__Music__Tv programmes__podcast__books__photos : click in photos
you will see SYN PHOTO FROM (Pictures)
Select : all folders and UNTICK SYN PHOTO FROM (Pictures) ! You will get the message asking if you want to remove all photos !
Connect your iphone to computer
Click on the "Library" button on top right of iTunes screen
-it should bring you to all of your music
Click on "iPhone" button on top right of iTunes screen (be careful not to eject your iPhone)
Click on "Photos" tab at top of iTunes screen
-your phone is probably set to sync all photos. here you can change setting to only sync 'selected albums, events...."
To sync your iphone changes, go to top of iTunes menu: File > Devices > Sync iPhone 5.
If you want keep the pictures in your computer BUT remove from your iPhone, I advice you to sync your iPhone with iTunes, then you manage your pictures manually (choose the pictures you want and you don't want to sync with your iPhone), then click Sync button.
It is not necessary to delete pictures from your computer!
Hope it will be helpful