Is the use of 'takes' and 'came back' in this sentence correct?

The present tense of "to take" here could not be interpreted in any way other than the historic present, and the context of the sentence is not likely to correspond to that; therefore the tense of "to take" should be the present perfect, the past, or the past perfect, depending on the context. The tense of "to come back" is proper.

---

Additional explanations prompted by user Deceptive facade's comment

I

In the context of the sentence inquired about, "take" (be necessary, be needed) is a stative verb (no action) and here is CoGEL's conclusion on such verbs (A Comprehensive Grammar of the English Language, p. 179, § 4.5):

"With stative verb senses, the present is used without reference to specific time: ie, there is no inherent limitation on the extension of the state into the past and future (unless such a limitation is indicated by adverbials or other elements of the clause). The STATE PRESENT, as we may call this category, includes general timeless statements, so-called 'eternal truths' ".

Examples of state present from CoGEL

• Honesty is the best policy
• Water consists of hydrogen and oxygen.
• Two and three makes five.

User LPH's additions to the examples, from OALD, 34 at the entry "take v." ([transitive, no passive] to need or require something in order to happen or be done)

• It only takes one careless driver to cause an accident. (all the time, any time)
• It doesn't take much to make her angry. (all the time, any time)
• (Compare) It didn't take much to make her angry. (user LPH's example; there is in this new sentence a reference to a specific time.)
• It takes barley to make beer. (user LPH's example)

As in the context of this coming back after 5 years, the present cannot be any of the other types (HABITUAL, INSTANTANEOUS, HISTORICAL) it has to be a state present, and that is not logical. Moreover, my personal feeling at the reading of this sentence using the present for "to take" is one of incongruity, and that appears to confirm the claims in CoGEL. Therefore, I wouldn't use the present, I do not think it to be right.

• It took an old friend who came back after 5 years studying in England to get her out of her shell.

II

There is a different interpretation, but it seemed that it couldn't be what was meant (on the ground of the description given in the text of the question).

(Free dictionary) get (one) out of (one's) shell

To cause one to be more outgoing. Usually said of a particularly shy or introverted person. Wow, I remember when Anna wouldn't even talk to anyone, and now she's likely to be voted "Most Talkative"—I wonder how the other kids got her out of her shell.

From this definition it is inferred that this state of being suddenly outgoing is more likely to be permanent; it has been triggered by the return, at one point in time. "It is only now when her friend is returning" forces the interpretation of "now" as "at the precise point of the return and of talking", or thereabouts (but approximated as being precisely that point for the purpose of grammar) (OALD, 1), and not as "from this point on" (OALD, 2). That is the assumption in "I".
        There is another possibility, but not reconcilable with the description given in the text of the question, which should then be something like "now after her friend's return": instead of this new state of lively humour being triggered once and for all and lasting, it is manifested as a succession of such states separated by a return to the usual gloominess, for instance on the repeated occasions of the meeting of the two persons. We are then dealing with a sequence of the necessary states of stimulation that pull her out of her gloominess, and not one. It is, on the basis of this assumption, possible to consider the habitual present as being the meaning conveyed: there is no limited time span in the future. Moreover, it is possible to add a frequency adverbial such as "always"; this is an indication that this verb of stative meaning can be used in a habitual sense (CoGEL, p. 180 § 4.6 Note [a]: Verbs of stative meaning may sometimes be used in a habitual sense when accompanied by a frequency adverbial (She is seldom alone.))

• It always takes an old friend who came back after 5 years studying in England to get her out of her shell.

(ref. 1) Remember that it always takes two to make a quarrel, and that the man who ...

(ref. 2) It always takes time with a new group to break the ice, lower their initial resistance, and reach the point where they are receptive enough to do good work.

This discussion about adverbs of frequency did not aim at saying that an adverb of frequency is needed, but only at showing that we are dealing with the habitual sense of the present. Here is for instance a case where no adverb is used, the sense being habitual.

(ref. 3) The Russian MI-24 Hind is a flying tank and it takes a cannon shell of 23mm or more in order to get through the armor to the pilots or the engine.

Therefore, along the line of this second interpretation you can use the present (habitual).

• It takes an old friend who came back after 5 years studying in England to get her out of her shell.