IPhone 5 not turning on, should I be worried? (new charger)?

The charger for my IPhone broke recently and I purchased a new one, which is a lightning braided one, after 3 days of not having any battery I've plugged in the new adapter and it's taking a while to turn on. Is this normal? I'm a new IPhone user and quite worried.

Have you tried turning it off and on again.

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