Yes, it is missing the word "for", that is relevant to the English grammar. I think. I am not a native English speaker, but that is what we learned at school.
"I lived in this house five years" is not incorrectly translated, it's just bad English. The correct would be "I lived in this house for five years."
Hmmm... Chiming in on the quandary. Learner of Turkish, and other languages. Native speaker of American English (Massachusetts). The "for " sounded, and still sounds, odd to my ear in the English sentence. Understandable but not the way we say it. On the other hand, "I HAVE lived in this house for five years " sounds just fine. Interesting. Thanks Duo!
To my non-native English speaker's ears, "I lived five years in this house" sounds better than the construction postponing " five years" at the end of the sentence. With or without "for". It is the same pattern applied to "Otobüsü bir saat bekledim" elsewhere in this exercise. Duo's preferred translation: "I waited an hour for the bus".
"For five years" is an English expression, expressing a certain course of time. The word "for" has several meanings in English. In this case it is used to indicate time or duration, like "He’s been famous for many decades." "I attended the university for one year only." "This is all I have for today." Turkish grammar does not need this preposition.
Other uses of the preposition "for" are to indicate the use of something (turkish word için) and to mean "because of" (cünkü).
To me at least, it sounds really odd to say "I live at this house." You could say "at this place," but "at this house" is quite unnatural.
I will say that if you are talking about where something is located, it is ok. (I lost my phone at this house, for example).