The programmer says that you need to use mysql 5.5.Is there a specific reason why you're looking for 5.5.66? The port was updated in August and is only a minor version behind the MySQL website (.62), so it's not exactly far behind, especially for a very old branch of MySQL.
The official MySQL downloads page offers 5.5.62 as the current version. The release notes page shows .62 and .63, but both are listed as not released (even though .62 clearly is) and there are no details in the change log.
I'm struggling to find anything at all about a .66 version.
===> mysql56-server-5.6.41_2 has known vulnerabilities:
mysql56-server-5.6.41_2 is vulnerable:
MySQL -- multiple vulnerabilities
CVE: CVE-2018-3286
CVE: CVE-2018-3283
CVE: CVE-2018-3284
CVE: CVE-2018-3282
CVE: CVE-2018-3279
CVE: CVE-2018-3278
CVE: CVE-2018-3161
CVE: CVE-2018-3186
CVE: CVE-2018-3280
CVE: CVE-2018-3212
CVE: CVE-2018-3170
CVE: CVE-2018-3200
CVE: CVE-2018-3173
CVE: CVE-2018-3162
CVE: CVE-2018-3277
CVE: CVE-2018-3171
CVE: CVE-2018-3174
CVE: CVE-2018-3187
CVE: CVE-2018-3247
CVE: CVE-2018-3195
CVE: CVE-2018-3185
CVE: CVE-2018-3144
CVE: CVE-2018-3145
CVE: CVE-2018-3133
CVE: CVE-2018-3203
CVE: CVE-2018-3137
CVE: CVE-2018-3182
CVE: CVE-2018-3251
CVE: CVE-2018-3156
CVE: CVE-2018-3143
CVE: CVE-2018-3155
CVE: CVE-2016-9843
WWW: https://vuxml.FreeBSD.org/freebsd/ec5072b0-d43a-11e8-a6d2-b499baebfeaf.html
1 problem(s) in the installed packages found.
=> Please update your ports tree and try again.
=> Note: Vulnerable ports are marked as such even if there is no update available.
=> If you wish to ignore this vulnerability rebuild with 'make DISABLE_VULNERABILITIES=yes'
*** Error code 1
Stop.
make[1]: stopped in /usr/ports/databases/mysql56-server
*** Error code 1
Stop.
I will wait, I hope the ports will be fixed quickly.MySQL 5.5 is vulnerable to the same things. As it's vulnerable to the exact same issues it should not be stopping you from migrating to 5.6 or 5.7. By the time you're done and your programmer is up to date these vulnerabilities are likely to be fixed.