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Subscriptions stack. If you buy on the 5th and you're set to expire on the 16th your new expiration date would still be the 16th. You'd be paying in advance but you'd still get a year.
If you let it end then renew you'll have access to all the games you downloaded again. You may need to renew the licenses by starting to redownload then canceling but they'll still be in your download list.
Actually you would have to renew licenses for previously download games after the end of your current subscription in either case. There is a grace period after your subscription ends during which you can purchase a new subscription and still keep all of the content that you previously received from your Plus subscription. It isn't clear how long it is, but it seems to be at least a couple of weeks. Your Playstation Plus online storage content is maintained for at least several months after your subscription ends, and you can retrieve it later by buying another subscription. You can renew your subscription before it expires, and the new subscription will start when the previous one ends; just as if you renewed automatically at the end of your current subscription. The exception is if you purchase a subscription during a 30-day free trial. In that case, the new subscription starts immediately; instead of at the end of the trial. If you are using a 30 day free trial, then you can just let the subscription auto-renew when it expires if you don't want to lose any free days.