Yes, it won't be able to connect to the public/outside interface ip from dmz host.
From dmz host, you would need to connect to the private/dmz host ip address, in your case 10.10.10.51)
The exchange server would either needs to resolve the mail relay server to its private IP, or using IP address to connect instead of dns name if it can only resolve to the public ip.
Are you using an internal or external dns server?
If you are using an external dns server, then you could configure the "dns" keyword on the static PAT/NAT statement that you configure for the mail relay.
eg:
static (dmz,outside) tcp interface 25 10.10.10.51 25 netmask 255.255.255.255 dns
Or, alternatively, if you can't resolve dns to its private IP, you can configure hosts file entry to resolve the mail relay domain name to its private IP on your exchange server.
Hope that helps.