A very useful tool for debugging programs is software Stepper. The pedometer will show you how the program is evaluated one step at a time. The pedometer works only for programs written in educational languages, so I changed your program a bit (I did not change the logic).
DrRacket . ( ). " ..." "". "Beginner".
"" ( + ).
(define (max-num lst)
(cond
[(= 0 (length lst)) "Your list is empty!"]
[(= 1 (length lst)) (car lst)]
[(>= (car lst) (cdr (car lst))) (max-num (list (car lst) (car(cdr lst))))]
[else (max-num(cdr lst))]))
(max-num (list 1 2 3 4 5))
(max-num (list -5 -3 -2 -13))
, .