Hi Bay Taner and welcome to the forums!
Yours is a bit older than the oldest machine I've run Stardew on, which is a Core 2 Duo Mac from 2009. The processor will probably be fine but the video card is the real question mark. Looking it up, its release date is in 2008, about the same time as for my oldest machine but that machine only runs the legacy version of Stardew. This I believe is v1.5.6, not the current v1.6.15 but v1.5.6 is still a great version of the game! Luckily that version is still available through Steam and while your machine is not the fastest, neither is mine and yours should run similarly well.
Edit: wow I opened Steam and there's like loads of versions, including a newer legacy 1.6.8 version which may run on your machine and give you all the v1.6 updates! There's also a Compatibility version but no version number is listed. One of these should work. Cross fingers!