The "SearchAddress" method does a free form query on the input and tries to determine what it is. This is good if you have address strings. In your case you know the input will be a zip code, so you can use a structured address search:
var credential = new AzureKeyCredential(subscriptionKey);
var _searchClient = new MapsSearchClient(credential);
var result = await _searchClient.SearchStructuredAddressAsync(new StructuredAddress()
{
PostalCode = "80201"
});
Note that 5-digit zip codes are used in several countries around the world and many values exist in more than one country. With that in mind, it is useful to specify the country region information to focus the query. For example;
var result = await _searchClient.SearchStructuredAddressAsync(new StructuredAddress()
{
PostalCode = "80201",
CountryCode = "US"
});