Yes, that's a coincidence!

@Ashish Siva when can I pick up my car?

Now, imagine if the code is $12345$ , and the $10$ generated numbers are like this:

$\color{#D61F06}{1}9999,\;\color{#D61F06}{1}9999,\;9\color{#D61F06}{2}999,\;9\color{#D61F06}{2}999,\;99\color{#D61F06}{3}99,\;99\color{#D61F06}{3}99,\;999\color{#D61F06}{4}9,\;999\color{#D61F06}{4}9,\;9999\color{#D61F06}{5},\;9999\color{#D61F06}{5}$

We can see that each digit of the actual code should appear on $2$ generated numbers on average

Now, notice that for the $10$ generated codes:

$\color{#D61F06}{1}4073,\;\color{#D61F06}{7}9588,\;\color{#D61F06}{0}5892,\;\color{#D61F06}{8}4771,\;\color{#D61F06}{6}3136,\;\color{#D61F06}{4}2936,\;\color{#D61F06}{3}7145,\;\color{#D61F06}{5}0811,\;\color{#D61F06}{9}8174,\;\color{#D61F06}{2}9402$

The first digit of the codes are all different, which implies that only $1$ number has the correct first digit. This in turn implies that one of the digits in the correct position appears on $3$ distinct generated numbers. We check for this, and find two possible cases:

$140\color{#EC7300}{7}3,\;79588,\;05892,\;847\color{#EC7300}{7}1,\;63\color{#20A900}{1}36,\;42936,\;37\color{#20A900}{1}45,\;50811,\;98\color{#20A900}{1}\color{#EC7300}{7}4,\;29402$

Either the $3^{\text{rd}}$ number is $\color{#20A900}{1}$ , or the $4^{\text{th}}$ number is $\color{#EC7300}{7}$ . No other method, we gotta do a case by case analysis

---

Case 1: $3^{\text{rd}}$ number is $\color{#20A900}{1}$

Now, we know that the $4^{\text{th}}$ number cannot be $\color{#EC7300}{7}$ . This implies that the remaining correct digits each appear in $2$ distinct numbers. We check the $5^{\text{th}}$ digit for such a number:

$14073,\;79588,\;0589\color{#3D99F6}{2},\;8477\color{#69047E}{1},\;\color{#20A900}{63136},\;42936,\;\color{#20A900}{37145},\;5081\color{#69047E}{1},\;\color{#20A900}{98174},\;2940\color{#3D99F6}{2}$

We have two possibilities: $\color{#69047E}{1}$ or $\color{#3D99F6}{2}$

Suppose that the $5^{\text{th}}$ digit is $\color{#69047E}{1}$ :

$14\color{#27D2E7}{0}73,\;79\color{#27D2E7}{5}88,\;05\color{#27D2E7}{8}92,\;\color{#69047E}{84771},\;\color{#20A900}{63136},\;42\color{#27D2E7}{9}36,\;\color{#20A900}{37145},\;\color{#69047E}{50811},\;\color{#20A900}{98174},\;29\color{#27D2E7}{4}02$

The remaining $3^{\text{rd}}$ digits are all distinct, therefore this combination is not possible

Instead, we try $\color{#3D99F6}{2}$ as the $5^{\text{th}}$ digit:

$14\color{#27D2E7}{0}73,\;79\color{#27D2E7}{5}88,\;\color{#3D99F6}{05892},\;84\color{#27D2E7}{7}71,\;\color{#20A900}{63136},\;42\color{#27D2E7}{9}36,\;\color{#20A900}{37145},\;50\color{#27D2E7}{8}11,\;\color{#20A900}{98174},\;\color{#3D99F6}{29402}$

Similarly, the remaining $3^{\text{rd}}$ digits are all distinct, therefore this combination is not possible too.

We can conclude that Case 1 is not possible, and the correct answer lies in Case 2

---

Case 2: $4^{\text{th}}$ number is $\color{#EC7300}{7}$

The $3^{\text{rd}}$ number cannot be $\color{#20A900}{1}$ , and the remaining digits appear in two numbers each. We repeat the same steps earlier:

$\color{#EC7300}{14073},\;79588,\;0589\color{#E81990}{2},\;\color{#EC7300}{84771},\;6313\color{#BBBBBB}{6},\;4293\color{#BBBBBB}{6},\;37145,\;50811,\;\color{#EC7300}{98174},\;2940\color{#E81990}{2}$

It can be $\color{#E81990}{2}$ or $\color{#BBBBBB}{6}$ .

We test the number $\color{#E81990}{2}$ first:

$\color{#EC7300}{14073},\;7\color{#27D2E7}{9}588,\;\color{#E81990}{05892},\;\color{#EC7300}{84771},\;6\color{#27D2E7}{3}136,\;4\color{#27D2E7}{2}936,\;3\color{#27D2E7}{7}145,\;5\color{#27D2E7}{0}811,\;\color{#EC7300}{98174},\;\color{#E81990}{29402}$

The remaining $2^{\text{nd}}$ digits are all distinct, therefore this combination is not possible

Therefore, we know that the $5^{\text{th}}$ digit must be $\color{#BBBBBB}{6}$

$\color{#EC7300}{14073},\;7\color{teal}{9}588,\;05\color{magenta}{8}92,\;\color{#EC7300}{84771},\;\color{#BBBBBB}{63136},\;\color{#BBBBBB}{42936},\;\color{#D61F06}{3}7145,\;50\color{magenta}{8}11,\;\color{#EC7300}{98174},\;2\color{teal}{9}402$

From here, we can decude the remaining digits. The $2^{\text{nd}}$ digit must be $\color{teal}{9}$ , and the $3^{\text{rd}}$ digit must be $\color{magenta}{8}$ . This leaves us with $\color{#D61F06}{3}$ as the $1^{\text{st}}$ digit

---

$140\color{#EC7300}{7}3,\;7\color{teal}{9}588,\;05\color{magenta}{8}92,\;847\color{#EC7300}{7}1,\;6313\color{#BBBBBB}{6},\;4293\color{#BBBBBB}{6},\;\color{#D61F06}{3}7145,\;50\color{magenta}{8}11,\;981\color{#EC7300}{7}4,\;2\color{teal}{9}402$

Ashish's car entry code is $\large\boxed{\color{#D61F06}{3}\color{teal}{9}\color{magenta}{8}\color{#EC7300}{7}\color{#BBBBBB}{6}}$

This problem can be easily solved using a brute-force search through all possible 5-digit codes and comparing them with the given generated numbers. This isn't a solution that uses extensive application of logic, but I think it is a valid solution nonetheless.

from itertools import permutations

givens = ["14073", "79588", "05892", "84771", "63136", "42936", "37145", "50811", "98174", "29402"]
for p in permutations([1, 2, 3, 4, 5, 6, 7, 8, 9, 0], r = 5):
    s = ""
    for c in p: s += str(c)
    counts = 0
    for g in givens:
        digits_in_common = 0
        for i in range(5):
            if s[i] == g[i]: digits_in_common += 1
        if digits_in_common == 1: counts += 1
    if counts == len(givens):
        print(s)
        break

The program above outputs $\boxed{39876}$ .