"There are gifts in the box."
Translation:В коробке подарки.
Because that was "Dima is in the taxi", not "there is a Dima in the taxi".
When you inform a listener about the existence of some new object (often expressed by "there is/there are" in English) you put this object in the end of the sentence. If you talk about a known thing (expressed by the definite article in English, or, in the case of "Dima" you just assume we know who we are talking about) the neutral SVO (Subject-Verb-Object) word order is used.
"There are gifts in the box." - "В коробке подарки."
"The gifts are in the box." - "Подарки в коробке."