An analogy:
People first got access to the internet in their homes using dial-up modems, where everything took ages to load because the data transfer rate was so slow. Then things got a lot better with the arrival of broadband services through conventional copper cables, where data could be transferred much faster. For those that need it (and not everybody does), things got even better with the arrival of super-fast broadband, where data is transferred through fibre optic cables.
There have been similar advances in mobile technologies over the years, as we've moved from 2G phones and phone masts (which could only transfer data very slowly), through to 3G, 4G and 5G ones, with each advance seeing faster data transfer speeds than before. So 5G is just a way of getting data to your phone faster than could be done with 4G.
However 5G hasn't been rolled out to the whole country yet. Each phone service provider (EE, O2, Vodafone, etc) is moving at their own pace but it's generally only major cities, together with larger towns, where 5G reception is available. (So having a 5G phone and SIM is completely pointless at the moment if you don't live in, or regularly visit, those places).
Many providers either don't currently support 5G services at all (e.g. Asda Mobile) or charge more to use them (e.g. Tesco Mobile). Those that do offer 5G normally use different SIMS. Assuming that your service provider follows that model, your old SIM will work perfectly well in your new phone but you'll only get a 4G service, not a 5G one.
You'll therefore need to decide whether or not that actually matters to you. If you don't live in, or work in, an area with 5G coverage, there's clearly no point in worrying about 5G until you can actually receive the service. Also, if you're perfectly happy with the time it takes for web pages to load on your phone using 4G, and streaming services (such as YouTube) already work well for you, you might decide that you don't need 5G at all and you can then stick with your old 4G SIM.
However if you actually want to have access to a 5G service, all you need to do is to insert the new SIM into your phone and then get your service provider to move your old number across to the new SIM. (It's a very simple procedure. Just give them a call).