Slainte (pronounced "SLAWN-cheh") is "Cheers!" "Bottoms Up!", etc. Gaelach means the historic people and language of Ireland. I'm guessing a very close translation would be "To your Irish health!", but that is a guess.
ANOTHER ANSWER;
It looks a lot like the common Irish phrase "Sláinte geal" or "Bright Health" as in a toast. "Sláinte Gaelach" doesn't sound correct. Perhaps it was misheard.
Slainte means cheers to good health
It means "Irish pride".
rinceoir Gaelach ordamhsóir Gaelach.
Mo bhanphrionsa Gaelach = my Irish princess.
"gaelach" should be "na nGael" "Ádh mór na nGael a thabhairt duit" means "To give you good Irish luck"
This looks like someone who doesn't speak Irish or possibly google translator. "Do léigh" read, as in past tense of 'read' "gaelach" means Irish or Gaelic as an adjective, not a noun. You tell me.
Stobhach Gaelach
Ceol Gaelach
Gaeilge for the language; Gaelach as an adjective.
Croí Éireannach or Croí Gaelach
It is pronounced as "stoh-vakh gay-lakh."
"Conrós Gaelach" or "Conrós Éireannach"