It is hard to evaluate pearls that are photographed against a dark background-- it just swallows up the luster and details.
Could you take some more photos, this time against a white background (like a paper towel)? No flash, in focus, and please include some close-ups especially of any blemishes you see.
I don't suppose you have the clasp? Unfortunately without a Mikimoto clasp there is no way to know if they are Mikimoto brand pearls specifically, or if they are unbranded pearls that were stored in that box.
I also can't tell from that photo whether they are real pearls or imitations. They are very consistent in their shapes, colors, surface... which could be turned of good cultured pearls, but also of imitations.
Again, more photos will help.
Also please try rubbing two of the pearls together gently and see what you feel. Imitation pealrs tend to glide against each other smoothly while real pearls feel a bit gritty.