"How" do I exercise a Call option?

Say, now it's May and XYZ company's share price is $50, and I bought its Oct $52 (striking price) Call option at $2.5 (premium). Two months later, if the share price goes up to $57 and I decide to exercise it, I suppose (from many investment books and online knowledge) I will have $2.5 profit per share (i.e., $57 - ($52 strike + $2.5 premium) ). However, I've seen demos on several brokerages' websites (as you can tell I'm new to this) and I'm really confused... By the time I try to exercise a Call option (not as I bought), after choosing 'sell to close' as an action, I will be also asked to enter a 'premium' again; what if the premium has also gone up (say $5 for XYZ companys Oct $52), what premium should I enter (again, upong exercising, not buying)? What's the significance of that premium (that is, what role does it play when I exercise my option)? Because of it, will I profit more? or will I lose part of my profit? Can anybody answer my question? Many thanks!

If you want to exercise an option do not choose the "sell to close" option.

"Sell to close" means that you simply want to sell the option without exercising it.

Exercising a call option means that you will buy the stock at the striking price.

Exercising a put option means that you will sell the stock at the striking price.

There is usually some "time premium" included in the price of the option, so if you simply want to take your profit from your position you are usually better off with a "sell to close" transaction instead of exercising the option.

If you use a sell to close limit order the premium you enter is the minimum price at which you are willing to sell the option.

The method you need to use to exercise an option will depend on the brokerage. You will need to specify which option you want to exercise and how many contracts you want to exercise, but you will not need to specify a premium.

If you buy the option in May and now 2 months later the stock is higher in value, so will the value of the option, so it is much better to just sell the option and make the profit. Very few people will exercise an option in July that does not expire until October. Option exercises normally take place right before the option expires.