Murphydog is on the button. I have #77811, less than 250 away from your #78057. It is also a nickel finish. It shipped February 16, 1956. Collector talk labels it as "Improved I-Frame, Model of 1953" and "Pre-Model 32".
AFAIK the factory called them "The S&W Terrier". The one you are looking at seems to be in very good condition, and the nickel looks to be original (check for the telltale "N" marking on the left side of the grip frame under the grip, on the cylinder under the ejector star, and on the barrel flat in front of the SN...... that's where mine are, anyway). Original finish is important relative to value. You may also wish to verify that the stocks are numbered to the gun. The SN should be on the inside of the right stock panel, and should match the SN on the butt.
Attached is a copy of page 24 from the S&W Centennial Catalog dated 1952. The catalog picture front sight is half-round, and it is likely a five-screw, as the picture was of an example prior to the first batch of major engineering changes which altered the trigger guard, butt frame length,etc. but you can get a good sense of what S&W had to say about them at the time.
Check for the "N" to verify original nickel finish and let us know.
That's an attractive piece you are looking at.
Just be advised that the Terrier can be somewhat addicting.
Catalog Page:
A picture of SN 77811