住着工作了五年 or 住和工作了五年 are not idiomatic in Chinese. You should refer to fyl's suggestions.
【A】着【B】, means you are doing B while doing A. 住 generally means "to stay and sleep in a house". To us, you are not "working" while "staying in the house".
【A】和【B】, both 【A】and【B】 should be noun phrases. Verbs should not be connected by 和.
Personally, if I hear 她在美国生活和工作了五年, the sentence would sound fine to me, perhaps because the verbs are both in a two-character form. (In Chinese, one character usually represents one syllable.)
According to this, which I didn't know very well before, 和 can be used to join two verbs but normally this is limited to verbs both with two syllables. In our example, 生活 and 工作 have two syllables respectively, which might be the reason why they can be joined by 和. (Please also note that according to its explanation, normally, two-syllable verbs that are joined by 和 cannot function as the predicate alone without adding necessary sentence elements such as adverbials, objects, etc. as part of the predicate.)
So perhaps if we say 她生活和工作, it would be wrong. If we say 她在美国生活和工作了五年, it would be correct since there're adverbials 在美国 and 五年 in this sentence.
Please also follow other members' good suggestions of not using 和 to connect two verbs, when you're not very sure.
Verbs can be connected by 和 . 和：（一）连接并列成分，表示平等的联合关系，可连接名词性词语，也可以连接动词性词语。
他曾经在美国学习和工作五年。 or 他在美国学习和工作过五年。 or 他曾经在美国学习和工作过五年。
In order to be more accurate ,without context ,you need to add 曾经 or 过 or both of them to the sentence.
I have seen an article that says 和 can connect verbs that have similar or opposite meaning.
Yes, It's not suitable for every case. For example ,他被扣押并写下检讨. 和 can not be used here for 扣押 and 写 are quite different.
I think 生活/ 学习 and 工作 are similar,和 can be used. But 居住 and 工作 is different, 和 can not be used.
^I think 和 is fine to connect verbs or verb phrases only under the following conditions:
1. the two verbs or verb phrases are considered "actions" or "events", which means they are exactly like "verbal nouns".
2. the two acts occur to the same subject,simultaneously and have absolutely equal status.