The instinct is understandable, and it is the right instinct almost everywhere else in business. If one supplier says no, you ask five more. Casting a wider net is how most problems get solved.
Lending is the exception, and the reason is structural rather than a matter of etiquette. Five suppliers assess you independently, in ignorance of each other. Five lenders do not. Each one pulls your file, and that pull is recorded as a credit enquiry before the next lender reads it. A cluster of enquiries in a short window is therefore visible to everyone who looks afterwards, and it is read as a signal about your circumstances — often before anyone has assessed the business at all.
How that recording works, how long it is kept, and what it does to a credit grade is a separate subject with published sources, and we have set it out in full on its own page rather than compressing it here: does applying to multiple banks hurt my credit grade? Read that one for the mechanism. This page is about what to do with it.
Before approaching a bank, ask what information it needs and whether a formal application will involve a credit check. An initial conversation and a formal application are different steps.