If you're trying to decide between the Series 3 and Series 5, it's worth thinking about exactly what you want to get out of the watch — and of course, how much you're willing to pay for it.
The Series 5 is better suited for those who may need a watch that fulfills specific use cases in addition to offering all of the basics. For example, those who may want to capture more precise data about their heartbeat rhythms and share it with their doctor should look at the Series 5 since it has an electrical heart sensor. (That's in addition to an optical heart sensor for measuring your heart rate, which the Series 3 also has.)
The Series 5 may also be the right choice for those who travel frequently and have the budget to opt for a pricier model, considering it has an integrated compass for showing your location more precisely and international emergency calling.
The other upgrades that come with the Series 5 make using the watch feel more convenient, but probably aren't worth the gap in price alone. The Series 5's screen is larger than that of the Series 3, making it easier to cram more complications on the display and therefore see more information at a glance. The display also stays on even when it's not activated, making the Apple Watch better at its most important job — telling the time.
Taken together, those changes make the Apple Watch Series 5 a much more capable smartwatch. But it's hard to compete with a watch that offers many of the same features and a similar experience for half the price.
Those who don't need specific features like a built-in compass or EKG monitoring and don't mind missing out on an always-on display will probably be just as happy with the Series 3. That older watch can still track your workouts and activity, display text messages and notifications from your phone, run apps, launch Siri on the wrist, and do almost everything else the Series 5 can.