Since Adele has 30 albums, and Bridget has 15 fewer, Bridget has 30-15= <<30-15=15>>15 albums.
Together, Bridget and Adele has 30+15 = <<30+15=45>>45 albums.
Katrina has six times the number of albums as Bridget, a total of 15*6= <<6*15=90>>90 albums.
Adele, Bridget, and Katrina have a total of 90+45 = <<90+45=135>>135 albums together.
Miriam has five times the number of albums as Katrina, a total of 5*90 = <<5*90=450>>450 albums.
Together, Adele, Bridget, Katrina, and Miriam have 135+450 = <<135+450=585>>585 albums.
#### 585