Exhibit 5.1

[Form of Opinion of Carey y Cía Ltda.]

November [—], 2014

MetLife Chile Acquisition Co. S.A.

Agustinas 640, 22^nd floor

Santiago, Chile

Ladies and Gentlemen:

We have acted as special Chilean counsel for MetLife Chile Acquisition Co. S.A. (“Acquisition Co.”) a closely held corporation organized under the laws of the Republic of Chile, on the prospective merger by incorporation of Administradora de Fondos de Pensiones ProVida S.A. (“ProVida”) into Acquisition Co. (the “Merger”). Upon effectiveness of the Merger, the absorbing company (“Nueva ProVida” or “the Company”) will proceed to the issuance of 22,387,807 shares without nominal (par) value of the Company (“Shares”).

We are giving this opinion in connection with the Registration Statement on Form F-4 (Registration No. 333-[—]) filed by Acquisition Co. with the U.S. Securities and Exchange Commission on November 19, 2014 (the “Registration Statement”) to effect registration of the Shares pursuant to the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder (the “Act”).

In rendering the opinions expressed below, we have examined the following agreements, instruments and other documents:

(a) the Merger Agreement, executed on November 14, 2014, by and among Inversiones MetLife Holdco Dos Limitada, Inversiones MetLife Holdco Tres Limitada, and MetLife Chile Inversiones Limitada as the sole shareholders of Acquisition Co., on the one hand, and Acquisition Co., as ProVida’s controlling shareholder, on the other.

(b) the minutes of the Board of Directors meetings of Acquisition Co., held on November 12 and November 17, 2014.

(c) the minutes of the Board of Directors meeting of ProVida, held on November 17, 2014.

(d) copies of the bylaws of Acquisition Co. and ProVida, and all the corporate minutes with respect to the issuance of Nueva ProVida’s shares.

(e) such other documents as we have deemed necessary for the purposes of the opinion expressed below.

In giving the opinions below we have assumed (without independent investigation on our part):

(a) the genuineness of all signatures thereon;

(b) the legal capacity of all individuals;

(c) the authenticity of all documents and records presented as originals, and the conformity with the originals of all documents and records presented as copies.

Based upon the foregoing, and having regard to legal considerations that we deem relevant, we advise you that in our opinion:

(1) Upon the effectiveness of the Merger and provided that (i) the Merger has been authorized by the Chilean Superintendency of Pensions (Superintendencia de Pensiones), (ii) the Chilean Superintendency of Securities and Insurances (Superintendencia de Valores y Seguros) has registered the issuance of the Shares, and (iii) the Merger is completed in accordance with the Merger Agreement, the Shares will be validly issued, fully paid and non assessable.

(2) Subject to the qualifications stated herein and therein, the discussion in the Registration Statement under the heading “Part Three - The Merger - Material Chilean Tax Consequences”, insofar as it describes certain Chilean tax consequences of the Merger to Foreign Holders, constitutes our opinion with respect to the Chilean tax consequences to a Foreign Holder of ProVida common stock of the merger of ProVida with and into Acquisition Co. and the subsequent ownership, if any, of Nueva ProVida Shares.

The foregoing opinions are subject to the following qualifications:

(a) We are qualified to practice law in Chile and we do not purport to be experts in or to express any opinion herein concerning, any laws other than the laws of Chile that are currently in effect. In particular, we have made no independent investigation of the laws of the United States of America or any state thereof as a basis for our opinion, and have assumed that there is nothing in any such laws that affect our opinion.

(b) With respect to matters of fact, we have relied upon the representations, opinions and certificates of officers of Acquisition Co. or other written statements of officials of jurisdictions having custody of relevant documents.

(c) This opinion letter is effective only as of the date hereof. We assume no obligation to advise you of any development or circumstance of any kind, including any change of law or fact that may occur after the date of this opinion letter even though such development, circumstance or change may affect the legal analysis, a legal conclusion or any other matter set forth in or relating to this opinion letter. Accordingly, any person relying on this opinion letter at any time after the date hereof should seek the advice of its counsel as to the proper application of this opinion letter at such time.

We hereby consent to the filing with the U.S. Securities and Exchange Commission of this opinion as an exhibit to the Registration Statement, and to the references made to our firm under captions “Part Six - Legal Information - Validity of Nueva ProVida Shares” and “Part Three - The Merger - Material Chilean Tax Considerations” and in the Prospectus which is included in the Registration Statement. In giving such consent, we do not thereby admit that we are experts with respect to any part of the Registration Statement, including this exhibit, within the meaning of the term “expert” as used in the Act, or the rules and regulations of the U.S. Securities and Exchange Commission issued thereunder.

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This opinion letter is provided to you by us in our capacity as special Chilean counsel to Acquisition Co. and may not be used for any purpose other than in connection with the transactions described in the Registration Statement without, in each instance, our prior written consent.

Very truly yours,

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