First, 실망하다 - be disappointed at someone/something
well it’s hard to explain in Englis... but I hope this will help you!
섭섭하다 - For example, you can use this as you graduate a school, you would feel sad a little bit. whether you liked it or not, a graduation means you finally say good-bye to your past! - 졸업한다니 시원 섭섭하네. 이제 이 집을 떠난다니 섭섭하다.
서운하다 - when someone hurts you mentally and you feel sad inside. like when someone close to you forgot your birthday, you can say like this. - 너한테 서운하다 내 생일도 잊어버리냐.
속상하다 - it means upset and sad. it is likely to be related to unfair situations than others.나는 내가 잘못한것도 아닌데 혼나서 속상했어. 속상하니까 기죽지마! 돈없다고 무시해 속상해.
슬프다 - it can used in the widest range among these. it can replace the other expressions(but specific expressions would be nicer to deliver you exact feelings) 졸업한다니 슬프네, 혼나서 슬펐어, 슬프니까 기죽지마. but ‘너한테 슬프다’ this doesn not gramatically feel right, it’s just awkward.