I live very close to this shopping mall.

[Silverobama]

There’s a shopping mall very close (5 minute walk). to where I live.

Is it natural to say “I live very close to this shopping mall”?

 

[Rover_KE]

Only if the person you're saying it to is in the shopping mall with you.

 

[teechar]

... or for example, if you're pointing to a picture of that shopping mall on a map.

 

[emsr2d2]

There’s a shopping mall very close (5 five minutes' walk) no full stop here to where I live.

Remember to write the numbers zero to twenty in words, not digits.
Use either "five minutes' walk" or "a five-minute walk".

Is it natural to say “I live very close to this shopping mall”?

The others have given you the contexts in which "this" works. If someone has already mentioned the name of the mall, you'd say "... close to that shopping mall".