Hey guys,
I am trying to do this quest to become thane of solitude but the quest is stuck at 4/5. No matter what I do to help people in solitude I can't get it to get to 5/5. Has anyone encountered this bug? Is there a workaround? Thanks

I've not had problems with this one, but I will list the things (that I can remember) which I think added to the total.
1. There is a person walking around the Bard's college who needs help (the Sheagorath quest)
2. A woman who has a stall in the market, needs her spiced wine shipment freed up.
3. The Jarl's steward has at least two quests for you (they are related to a Necromancer).
4. Not sure if the Bards college quests help, but try those (there is a festival that has been cancelled, which the people of Solitude want to return).
5. If I remember correctly, the jarl has a special quest for you (I think she needs you to fetch something of her dead husbands).
6. Try the argonian, and his 'lighthouse' quest.
7. There is an old woman who is grieving and needs consoling, who can be found walking around (note that when I tried this, it didn't complete properly, but didn't me affect getting 5/5).
8. Some of the shop-keepers have random quests, like fetching certain ingredients, or checking upon the daughter who is in Whiterun/riverwood (can't remember the details, but she is in the alchemists shop, Note that depending upon the time of day, the person in the shop that you get the quest from, may be different. You are looking for the older woman).
9. Taurie has a quest for you, as she wants you to get the Jarl's opinion on an outfit.
10. Possibly, Sam Geuvere (or something like that) has a quest for you, and can be found in the Winking skeever, if you are past level 14.

Give those a try. In particular, check the Jarl. I think I had 4/5 for a while and didn't know how to get the final quest. Talking to the Jarl gave me the final quest.

Thanks, I just kept doing quests and eventually I managed to get one to trigger the 5/5.