Five number code

I have a 5 digit code on the bag that I forgot. All I remember is that it was a symmetric number and the sum of its digits was 22. Write all the numbers that can be a code. .

Correct answer:

n =  41

Step-by-step explanation:

$$\begin{gathered} n=41 \\ {n}_1=16861 \\ {n}_2=17671 \\ {n}_3=18481 \\ {n}_4=19291 \\ {n}_5=25852 \\ {n}_6=26662 \\ {n}_7=27472 \\ {n}_8=28282 \\ {n}_9=29092 \\ {n}_{10}=34843 \\ {n}_{11}=35653 \\ {n}_{12}=36463 \\ {n}_{13}=37273 \\ {n}_{14}=38083 \\ {n}_{15}=43834 \\ {n}_{16}=44644 \\ {n}_{17}=45454 \\ {n}_{18}=46264 \\ {n}_{19}=47074 \\ {n}_{20}=52825 \\ {n}_{21}=53635 \\ {n}_{22}=54445 \\ {n}_{23}=55255 \\ {n}_{24}=56065 \\ {n}_{25}=61816 \\ {n}_{26}=62626 \\ {n}_{27}=63436 \\ {n}_{28}=64246 \\ {n}_{29}=65056 \\ {n}_{30}=70807 \\ {n}_{31}=71617 \\ {n}_{32}=72427 \\ {n}_{33}=73237 \\ {n}_{34}=74047 \\ {n}_{35}=80608 \\ {n}_{36}=81418 \\ {n}_{37}=82228 \\ {n}_{38}=83038 \\ {n}_{39}=90409 \\ {n}_{40}=91219 \\ {n}_{41}=92029 \end{gathered}$$

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