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.
In Irish, 'slán agus sláinte'; in Scots Gaelic, 'slàn agus slàinte' meaning 'healthy and health'.
"Sláinte agus Beannachtaí" means "Health and Blessings"
"health and life to you" said to one person.
Sláinte means health/cheers.
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"
slawn-jih vah in Scots Gaelic (Good health!)
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.
Ceol Gaelach
Stobhach Gaelach
Gaeilge for the language; Gaelach as an adjective.
Croí Éireannach or Croí Gaelach
"Conrós Gaelach" or "Conrós Éireannach"