<PAGE>   1
                                                                     EXHIBIT 5.1

                          [SNELL & WILMER LETTERHEAD]

                               December 22, 1999

The Dial Corporation
15501 North Dial Boulevard
Scottsdale, Arizona 85260-1619

      Re:   Registration Statement on Form S-3

Ladies and Gentlemen:

      At your request, we have examined the Registration Statement on Form S-3
(the "Registration Statement") relating to the registration and sale from time
to time by you of up to an aggregate of $300,000,000 of debt securities, notes
and/or other evidences of indebtedness ("Debt Securities") of The Dial
Corporation in amounts, at prices, and on terms to be determined at the time of
offering. We have also examined the Indenture which was executed and delivered
on March 5, 1998, such corporate records, certificates and other documents and
such questions of law as we have considered necessary or appropriate for the
purposes of this opinion. Capitalized terms used but not otherwise defined
herein shall have the meanings ascribed to them in the Registration Statement.

      Based upon the foregoing, we advise you that, in our opinion, when the
following events have occurred:

     (a) The Registration Statement has become effective under the Securities
Act of 1933, as amended;

     (b) The due authorization, execution and delivery of the Supplemental
Indenture to the Indenture pursuant to which Debt Securities are to be issued.

     (c) The due execution, registration and delivery of the certificate or
certificates evidencing the Debt Securities; and

     (d) The Debt Securities have been established, issued and sold in the
manner specified in the Registration Statement and the exhibits thereto, in
accordance with corporate and governmental authorities and not in violation of
any applicable law, agreement or instrument; then

<PAGE>   2
The Dial Corporation
December 22, 1999
Page 2

      1. The Debt Securities to be issued by you will be legally issued under
the Registration Statement, will be legally issued and binding obligations upon
you, subject to the effect of (a) applicable reorganization or similar laws and
court decisions affecting creditors' rights and remedies generally and (b) the
application of general principles of equity (whether such enforceability is
considered in a proceeding in equity or at law).

      You have informed us that you intend to issue the Debt Securities from
time to time on a delayed or continuous basis. Accordingly, this opinion is
subject to the laws, including the rules and regulations, as in effect on the
date hereof. We understand that prior to issuing any Debt Securities you will
advise us in writing of the terms thereof, will afford us an opportunity to
review the operative documents pursuant to which such Debt Securities are to be
issued (including the applicable Prospectus Supplement) and will file such
supplement or amendment to this opinion (if any) as we reasonably consider
necessary or appropriate by reason of the terms of the Debt Securities.

      This opinion is intended solely for the use of The Dial Corporation in
connection with the Registration Statement. It may not be relied upon by any
other person or for any other purpose, or reproduced or filed publicly by any
person, without the written consent of this firm.

      We hereby consent to the use of this opinion as an exhibit to the
Registration Statement, and we further consent to the use of our name under the
caption "Legal Matters" in the Registration Statement and in the Prospectus and
the form of Prospectus Supplement.

                                       Very truly yours,




                                       SNELL & WILMER L.L.P.