Compared to the size of the Bitcoin ledger, the size of the Cardano blockchain is relatively small as of January 21, 2022. You can see the blockchain size if you look in the Daedalus wallet's folder called ../wallet/chain/immutable.
|-------------------|--------------------|--------------------|
| Network | Blockchain size | Number of blocks |
|-------------------|--------------------|--------------------|
| Cardano | 27 GB | 6,782,599 |
|-------------------|--------------------|--------------------|
| Bitcoin | 439 GB | 719,727 |
|-------------------|--------------------|--------------------|
What will the size of the Cardano ledger be in 5 years period, for instance, is very difficult to say. It depends on the number of transactions in each block, the speed of formation of the ledger (we know it is Hydra's patrimony) and the total size of the transaction. Currently, the transaction size should not exceed 16 KB, including metadata.
However, in the Basho era, the Tx size could potentially be increased up to 256...512 KB, due to the use of smart contracts and increased network throughput.