Your company does not own your phone number. If you used your personal phone number for business reasons, then your company does not have a right to take that number away from you.
However, while I very much sympathize with you wanting to keep your phone number, please keep in mind that this phone number is somewhat tainted now. You've been using it in email signatures for the past 5 years for your employer, so everyone who you sent an email to from your company email address will see it as an official way to contact your company. That's what your boss alluded to. For them, your phone number is now an official way for any customer you've been in contact with to contact them.
Let me ask you something: are you willing to get monthly, or maybe even weekly phone calls from customers of your former employer on your private number for the next couple of years? Are you willing to patiently explain every time that you've left your company and that they'll have to call a different number? Even when you're on vacation, at your child's birthday party or while celebrating your anniversary with your partner? And don't even consider exploiting this for your own gain by trying to poach customers from your previous employer. This is unethical and might be banned by your contract or even by state law. 42 states have a law that bans stealing trade secrets from your employer, and that usually includes customer lists.
These phone calls will come in frequently, during any moment of your work day (and possibly even outside of that), and I assume that you can find new employment quickly. Is your new employer willing to accept that customers from your previous employer will call you on your own phone number on a regular basis, potentially disrupting your coworkers, just so you can tell them to call a different company? Your new employer might even want you to try and convince these clients to check them out, which again might land you in a legal minefield.
Note: this is something that shouldn't have happened. The only reason this is happening is because your ex-employer tried to cheap out by forcing you to pretty much relinquish your phone number, without actually taking control over it. What your boss should have done 5 years ago is get you a separate work phone so that you can keep these separate. If your boss had done that, you wouldn't have this problem right now.
This is a mess right now. The apparently simple answer would be to refuse the request, but then you will likely end up being an unpaid receptionist for your previous employer for years to come. However, accepting the request would mean you need to tell all your friends from the past 15 years that you have a new number. Depending on how many of them you know through social media, that may be as simple as just making a Facebook post. In the long term, this might provide you with fewer problems. I won't recommend you a specific option, but I do want to provide you with a warning for a potential outcome of one of the options.