I'm on the fence about them. It's harder to evaluate pearls that are photographed against a dark background like that. A white or neutral light background is better.
I'll give you a few simple tests to try:
1. Rubbing test (also called the "tooth test", but please don't rub them against your teeth, as teeth are harder than pearls and can scratch them). Rub 2 of the pearls together gently. What do you feel? Real pearl nacre feels a bit gritty while imitation pearls glide smoothly against each other. If they feel sticky it could be accumulated grime causing that, so wipe them clean with a damp cloth and try again.
2. Temperature test. For this you need some more pearls, either pearls you know to be real or that you know to be fake. Real pearls are cooler than fake pearls. Place these and the other pearls in the same room for half an hour or so (so they are in the same temperature environment, to eliminate that variable.) Then touch each to your lips brielfy. What do you feel?
3. Loupe test. If you have a jeweler's loupe (10x magnifier) examine the surface of the pearls. Real nacre is very smooth looking under 10x power while fake pearls have a coarser looking texture.
Look for any areas where there may be flaking imitation coating with the bead underneath exposed.
If you see blemishes, take a close up photo.
Also, check the clasp, including the tongue of the clasp, for a metal mark-- 10k, 14k, 585 (which is 14k) 14/20 (gold filled), etc. It is unusual for imitation pearls to have a genuine gold clasp (though not unheard of; these look older, based on the condition of the thread, and gold used to be cheaper.) It is also unusual for real pearls to have a base metal clasp.