If you do not use custom key bindings, there is nothing you need to do to upgrade to v5. However, if you do, you need to update your key binding to call __fzf_search_current_dir with two new arguments:

# If you use custom key bindings, change this...
bind \cv '__fzf_search_current_dir'
bind --mode insert \cv '__fzf_search_current_dir'
# ...to this...
set --local search_vars_cmd '__fzf_search_shell_variables (set --show | psub) (set --names | psub)'
bind \cv $search_vars_cmd
bind --mode insert \cv $search_vars_cmd

See conf.d/fzf.fish for more details.

After much feedback around Search Git Log's Ctrl+l key binding conflicting with clear screen, I have decided to change its key binding to Ctrl+Alt+l. An alternative option I considered was just Alt+l, which is shorter but I realized conflicts with __fish_list_current_token, which is actually quite useful.