Just five? Now that's hard.
1. M*A*S*H (Johnny Mandel)
2. MillenniuM (Mark Snow)
3. Dynasty (Bill Conti)
4. The Cosby Show (Bill Cosby & Stu Gardner; Season 5 version)
5. Dr. Quinn, Medicine Woman (William Olvis)
I think that anytime you have to cite a specific season you've lost the point of the original question. IMO.
Not when a series uses entirely different stylelistic themes from each season.
And one should not the vast majority of themes cited in this thread -- including half by the original poster -- are NOT songs.
I just mean that a truly great theme song is iconic-if you hear the opening of the song you think of the show. When a show rotates its theme every season or two you lose the monolithic approach, leaving it malleable and, ultimately, rendering it unimportant. Certainly, such a series of themes fails to reach Top 5 status at the very least. Of the five shows you cite, only one brings music to my mind when reading the name-MASH.