Find the password

C# (.NET Core), 617 bytes, total attempts = 182255, score = 1185166

using System;namespace p{class C{static void Main(){var l=Console.ReadLine();int L=int.Parse(l);var g=new int[L];var p=n(g);for(int i=0;i<L;i++){g[i]=5;var d=n(g);var f=d-p;var s=f;switch(s){case 5:g[i]=0;d-=5;break;case-5:break;case 3:g[i]=1;d=n(g);f=d-p;if(f>0){g[i]=9;d-=2;}break;case 1:g[i]=2;d=n(g);f=d-p;if(f>0){g[i]=8;d-=4;}break;case-1:g[i]=3;d=n(g);f=d-p;if(f>0){g[i]=7;d-=4;}break;case-3:g[i]=4;d=n(g);f=d-p;if(f>-3){g[i]=6;d-=2;}break;}p=d;}n(g);}static int n(int[] g){foreach(var i in g){Console.Write(i);}Console.WriteLine();var s=Console.ReadLine();var d=int.Parse(s);if(d<1) Environment.Exit(0);return d;}}}

Hopefully C# in this format works for you. It is in the form of a complete program, so there should be a way to compile to an executable. Let me know if there's anything I can do to make it easier. Bytes are part of the scoring even though the Code Golf tag is removed so my official submission removes all the unneeded whitespace and useful names. My explanation below will use fragments of the ungolfed code:

Explanation

This program uses only a single helper method:

static int newGuess(IEnumerable<int> guess)
        {
            foreach (var item in guess)
            {
                Console.Write(item);
            }
            Console.WriteLine();
            var distanceString = Console.ReadLine();
            var distance = int.Parse(distanceString);
            if (distance < 1) System.Environment.Exit(0);
            return distance;
        }

This writes the guess to stdout, then reads the distance from stdin. It also immediately ends the program if a guess is the exact combination. I call it a lot. Next the initial setup:

var lengthString = Console.ReadLine();
int length = int.Parse(l);
var guess = new int[length];
var prevDistance = newGuess(guess);

This gets the length of the combination, then starts guessing with all 0s. Afterwards, it iterates through each digit in a for loop.

guess[i] = 5;
var distance = newGuess(guess);
var difference = distance - prevDistance;
var switchVar = difference;
switch (switchVar)

For each digit, it guesses 5, then decides on the next step based on how the distance changed since the previous guess (where that digit was 0).

case 5:
    guess[i] = 0;
    distance -= 5;
    break;

If the distance increased by 5, then 0 was correct for that distance. Adjust that digit back to 0. Altering the recorded distance manually prevents an extra guess.

case -5:
    break;

If the distance decreased by 5, then 5 is the correct digit and we move to the next digit immediately.

After that things are tricky. Using 5 and 0 for my initial guesses means that the remaining difference possibilities are 3, 1, -1, -3 with 2 possibilities for each, which need 1 additional guess to distinguish. Each of these cases takes a similar form

case 3:
    guess[i] = 1;
    distance = newGuess(guess);
    difference = distance - prevDistance;
    if (difference > 0)
    {
        guess[i] = 9;
        distance -= 2;
    }

Some of the numbers change, but essentially we try one of the two possibilities, and check whether the change was the correct one for that digit. If it wasn't, then the other digit is correct so we set that digit then adjust the difference manually.

This method means we should require, at most, 1 guess for the initial 0s, 2 guesses per digit, and then 1 final guess to ensure the last digit doesn't fall through.

It might be buggy though, it works as far as I've checked manually but that's no guarantee. Bug found and squashed thanks to Colera Su

C, 388 374 368 bytes, total attempts = 162751, score = 982280

char s[999];i;G;H;t;n;h;e;R(x){scanf("%d",x);}W(i,x,a){printf((i-n?0:4)+"%0*d%0*d\n",i,x,n-i,0);R(a);}S(k,i){if(!(t=e=k>4?s[i]=48:k<1?s[i]=53:!G?H=k,G=i:0)){for(;t++<n;)putchar(48|t==i|t==G);puts("");R(&t);t==h?W(G,e=1,&t):0;s[G]=t>h?53+H:53-H,s[i]=t>h^e?53+k:53-k;G=0;}}main(){R(&n);for(W(n,0,&h);i++<n;S(t-h+5>>1,i))W(i,5,&t);s[G]=53+H,puts(s+1),s[G]=53-H,puts(s+1);}

Python 2 and 3: 175 bytes, total attempts = 1005972, score = 5448445

This program takes ceil(log(n))*10 attempts per combination or every single digit takes 10 attempts (so, 333 takes 30 attempts).

N=int(input());o=0
def c(a):
 print("0"*(N-len(str(a)))+str(a))
 return int(input())
for j in range(N):m={c(i):i for i in reversed(range(0,10**(j+1),10**j))};o+=m[min(m)]
c(o)

Huge thanks to Colera Su for helping me with the input/output functionality.

Python Version of Challenge (Modified by OP).

I wrote a version of the lock code inside of Python. You can go ahead and use if you're trying to solve this in Python (like me). The following works in Python 2 and 3. It made a lot more sense just to implement lock as a class you can test against and I decided to create a generator function for guessing the inputs.

import sys

class Lock:
    def __init__(self, number):
        self.lock = str(number)
    def l(self): #lengthOfNumber
        return len(self.lock)
    def c(self, guess): #check a guess
        guess = str(guess)
        guess = "0" * (len(self.lock) - len(guess)) + guess
        difference = 0
        for i in range(len(self.lock)):
            d1 = abs(int(self.lock[i]) - int(guess[i]))
            d2 = 10 - d1
            difference += d1 if d1 < d2 else d2
        return difference

def masterLock():
    testdata = ["000","555","755","735","744","746"]
    for answer in testdata:
        yield Lock(answer)

class LockIO:
    def __init__(self):
        self.lock = int(input())
    def l(self):
        return self.lock
    def c(self, guess):
        guess = str(guess)
        guess = "0" * (self.lock - len(guess)) + guess
        print(guess)
        sys.stdout.flush()
        return int(input())

for l in masterLock():
    # Write your code here that tries to guess it
    #   When you're done testing you can unindent your code,
    #   replace "for l in masterLock():" with "l = LockIO()"
    #   and submit the code.
    # 
    # Examples:
    #  l.l()      # returns the length of the lock
    #  l.c("952") # returns the distance to the lock
    #  l.c(952)   #  number also works
    pass