Reverse DNS doesn’t work – NXDOMAIN

Looking at the IP addresses in your resolv.conf I get the feeling that your BIND server is on 192.168.1.52. As far as I can tell, you can't specify in resolv.conf something like "for these domains, use this name server". Basically, your BIND server will never be queried. As you can see in your dig lookup (which is incorrect, it is asking for a reverse DNS entry), it tries 80.58.0.33, which I assume is your provider's DNS server.

You already set up BIND as caching nameserver by using the 'forwarders' option, so what you need to do is have only 192.168.1.52 in the client PCs as nameserver.

To see if your BIND is configured correctly, try this:

dig example.test @192.168.1.52

You've set it up correctly on your server, but your server is not marked as authoritative for 123.5.253.159.in-addr.arpa. Your reverse DNS is managed by your ISP (the whole 5.253.159.in-addr.arpa zone):

; <<>> DiG 9.7.3-P3 <<>> ns 5.253.159.in-addr.arpa
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 43579
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 2

;; QUESTION SECTION:
;5.253.159.in-addr.arpa.        IN  NS

;; ANSWER SECTION:
5.253.159.in-addr.arpa. 86010   IN  NS  ns3.uxw.nl.
5.253.159.in-addr.arpa. 86010   IN  NS  ns4.uxw.nl.

You have 2 solutions to solve that:

1. ask your ISP to define the 123.5.253.159.in-addr.arpa record for you on their DNS (ns3.uxw.nl and ns4.uxw.nl),
2. ask your ISP to delegate the 123.5.253.159.in-addr.arpa record to your server, as per the RFC 2317, this is just a matter of defining a CNAME pointing to a new record on a new zone on your DNS (you then have to define this special zone on your DNS, your ISP will tell you how to name this new zone).

First solution is probably the quickest, but if you change your server's name in the future, you've got to ask them to change it again. Second solution is the most flexible, if your ISP is willing to support RFC 2317. If your ISP is providing you with more than a single address, reverse DNS can be delegated for all of them (the whole range) so you can be in charge. I'd recommend you to ask for that.

This similar question is worth reading.

Trivia: a few years ago (5, or 10 years back), some people were advocating against RFC-2317, because some DNS clients couldn't handle the reverse queries well. However, I don't think that is relevant anymore, RFC-2317 exists for about 15 years now.