Create shortcut for interactive compile command

Question

I know that we can start compile interactively using C-u M-x compile. Is there a way to start this whenever I run M-x compile? If that cannot be done, how do I create a shortcut to C-u M-x compile?

My current shortcut for M-x compile is:

(global-set-key (kbd "<f5>") 'compile)

This would execute normal compile (not interactive). Ideally, I would like to create a separate shortcut for interactive compile (for program that requires a lot of user inputs).

Please let me know and thanks for your help

Edit: I forgot the mention that my compile command is also customized based on mode hook. For example, below is how I customize it for C++ mode hook and Fortran mode hook:

(add-hook 'c++-mode-hook
        (lambda ()
        (set (make-local-variable 'compile-command)
            (concat "g++ -g -Wall -lm " buffer-file-name " && ./a.out"  ) )))




(add-hook 'fortran-mode-hook
        (lambda ()
        (set (make-local-variable 'compile-command)
            (concat "gfortran " buffer-file-name " && ./a.out"  ) )))

Answer 1

(global-set-key [f5] (lambda ()
                       (interactive)
                       (let ((current-prefix-arg '(4)))
                         (call-interactively 'compile))))