Couple problems here.
First, as techmom said, the term is excessive - I have had non-competes at all of my jobs, and the most restrictive has a two-year term.
Second, a non-compete for an internship? The whole point of internships is to give a no-strings-attached taste of what it’s like to work in an industry or for a company. By issuing a non-compete, they are basically saying that you aren’t allowed to apply what you learned later on.
Third, a non-compete for an unpaid position (internship or not) is almost certainly unenforceable. A non-compete is a contract, and the most fundamental criterion for creating an enforceable contract is the presence of, among other things, acceptance and consideration. The person issuing the contract is requesting the signer to accept the terms, but that party must have skin in the game as well - this is consideration.
For example, let’s say I am buying a car from you. We draw up a contract that says you will sell me your car on August 15, at 10:00AM at the police station. You draft it and I sign it. At this point, you have accepted my offer, but aside from a piece of paper, there is nothing that has bound us. You have all of your car, and I have all of my money; if you decide not to meet at the agreed-upon date/time/location, nobody has lost anything materially. I can’t sue you for reneging on your agreement because I haven’t given you anything. If, however, I give you a $500 deposit when I sign the contract, then the contract becomes binding - you have received something in exchange for something else but have not yet delivered the item. If you, then, renege, I can sue you to recover my $500.
In most instances, a non-compete is issued as an offer with payment for services rendered as the consideration. It meets the basic definition for enforcement. In your case, it does not. Your “employer” is not providing you with any materially significant payment (‘experience’ isn’t material), so there is nothing that employer can do to prevent you from competing. I’m not a lawyer, so take my advice with a grain of salt (basing this on a single contracts class I took in college)
Fourth, it may be worthwhile to figure out what ‘competitor’ means. The broader the definition, the less enforceable it is. My first company out of college considered any company offering services similar to its own as a competitor. Typically that means that you can work at the competitor but may not have contact with anyone in the division that competes - if you work in algorithm development at Bing, you can go work in UX design at Google but not algorithm development - but my company expanded it. That made the contract essentially unenforceable. My last company had a much narrower definition - I was not allowed to work in certain departments (generalized for definition purposes) at a finite, explicit set of companies.
At the end of the day, unfortunately, even if a contract is unenforceable, they can still have you sign it and can still come after you, even if it is frivolous. In my case, a company I wanted to work for said that I was a great candidate but wouldn’t touch me because of my non-compete. They knew that they would win the lawsuit, but they would have to pay hundreds of thousands of dollars in legal fees on my behalf and were unwilling to bother.
For you, I would choose not to sign this non-compete at all if you aren’t getting paid. If they offer you payment (even in the form of a bonus for signing), don’t accept a 10-year term… 10 years is literally half your life right now, and that is far too long to commit not to work for competitors. If you agree not to disclose information, not to steal clients, and not to work for a competitor for six months or a year, AND if you get paid for it, then consider signing.