Hi there
Totally a personal opinion, but I wouldn't want to take such a young baby on holiday abroad. There's the heat, the sun, and the worry about hygiene standards. The end of June, things will just really be hotting up.
There's also the thought about how good any medical facilities are - though I understand it's really high standard in Turkey. It's also not some third world backwater, you can get baby supplies in the supermarkets.
I wouldn't worry about leaving them for the week either. 18 is of course adult age, and sure they'll be totally fine. You soon get used to having a baby around remember, and at five months, he/she should be pretty much sleeping through by then.
You go enjoy your hol, they'll be fine, and - might sound harsh, but it was their decision to have children, it's one of the responsibilites and consequences which comes with that decision.
Course, if they decide to come, perhaps the holiday will really do them good, and you could perhaps "sit" for an evening and let them have a bit of a break maybe. Baby will surely be ok, but it's only my opinion - I personally wouldn't take one so young.
Hope you make the right decision anyway, and above all, have a great time.