Short Answer… YES & NO 
One of the most frequently asked questions on 5g is about the SIM card and whether or not you need a new SIM to access 5G services.
It is probably a confusing topic because different opcos have different stances.
Interestingly, all the different answers are technically accurate so far, making the topic slightly more confusing than it should be. 
So, let’s simplify it here, and clarify the topic as much as possible.
Starting from the main question: What are the requirements to access 5G?
Typically, we will need 5G coverage, 5G supported mobile phone, and a 5G supported SIM card.
Focusing on the last point, we can start analysis.
Technically speaking, the SIM cards in 3G (UMTS), 4G (LTE) and 5G (NRr) follow the same specifications named “Rel 99+” issued in 3GPP Release 1999 (first released 3G specifications).
That means, all “Rel 99+” USIMs can be used to access every generation of mobile networks, including 5G.
Such backward and forward compatibility is achieved by the carefully designed offloading of some computations and storage to mobile phones.
However, there are additional security aspects developed in 5G specifications.
Prajwol Kumar Nakarmi & David Castellanos from Ericsson issued an amazing detailed article 2021 about the No Need to change the SIM Card in 5G era from a security perspective (theoretically).
Practically, the actual levels of privacy and security will fully depend on what programs sit on the existing SIM and the actual required/accepted levels by each operator to provide 5G services to its subscribers.
As a result, we may find some opcos who will requested subscribers to get a new SIM for 5G phone, and we may also find others who will advise otherwise.
Apart from security aspects, we can see the variance of selected SIM based on the deployed flavor of 5G.
In Non-Standalone 5G NSA deployments, all operators used the same 4G SIM and did not ask subscribers to change.
And this, of-course because the dependency of 5G NSA solution on existing 4G infrastructure. But for Standalone 5G SA, the situation completely changed:
Indian Jio operator announced: “Users do not need to upgrade their Jio SIM card to experience Jio True 5G”.
American T-Mobile announced: !While your current SIM card is 5G compatible, it is not capable of using the 5G standalone technology we recently rolled out. To access Standalone 5G, the SIM card in your compatible 5G device must be Standalone 5G capable".
On the other hand, SIM Giant suppliers (Thales, Giesecke+Devrient, IDEMIA, Valid, Eastcompeace Technology Co., Ltd, Workz and more) have already started to manufacture 5G SIM cards that are totally compliant with 3GPP 5G Standardization and Trusted Connectivity Alliance Recommended 5G SIM to be ready for 5G SA deployments.