With `zsh`:
autoload zmv # best in ~/.zshrc
zmv -n '(<1-5>).*' 'Season $(($1))'
(remove the `-n` when happy)
Note that it calls one `mv` per file so it would be less efficient than the 5 `mv` commands of your question (unless you do a `zmodload zsh/files` beforehand to get a builtin `mv`).
A `perl`'s `rename` alternative:
rename -n '$_="Season $1/$_" if /0*(\d+)/' 0[1-5].*
(remove `-n` when happy)
Note that `rename` calls the `rename()` system call, so that only works to move files within the same file system (while `mv` will resort to copy+unlink when moving files across file system boundaries).
With `mmv` (moving across FS boundary is supported, but then note that not all attributes will be preserved and for symlinks a copy of the target file is created):
mmv -n '0[0-9].*' 'Season #1/'
(remove `-n` when happy)