need an irule to forward DNS requests based on FQDN

Try something like this instead:

when DNS_REQUEST {
  if { ([IP::addr [IP::client_addr] equals 10.10.10.0/24]) } {
    switch -glob [string tolower [DNS::question name]] {
        " www.domain1.com" -
        " www.domain2.com" -
        " www.domain3.com" -
        " www.domain4.com" -
        " www.domain5.com" {
            pool external_dns_pool
        }
        default {
            pool internal_dns_pool
        }
    }
  }
}