No, you can't use a 5G connection on a 4G smartphone. 5G and 4G are not created with the same technology, so it will be practically impossible for the 5G network to work on a 4G smartphone. In other words, smartphones that use 4G LTE are designed in such a way that they are incompatible with the next generation of wireless mobile networks.
The technology is going to work perfectly on new phones that are designed to use 5G networks. The issue here is that 5G networks are yet to be rolled out to all parts of the world, so only a few people are using the technology.
But very soon, a lot of smartphones that support 5G networks will be made for people to buy. On the other hand, it is possible for a 5G smartphone to use the 4G network. The fact that you can easily switch to the 3G network even with a phone that uses 4G means you can equally use the 4G network on a 5G smartphone.