Are the following sentences correct?

They are correct, but each sentence must be understood in the right context.

1. The person is looking ahead or perhaps planning for the future and intends to visit 5 countries during the course of the year.

2. The second sentence may be used in the context of a person who has an objective or an activity in Japan in view and who hopes that by the time he completes it, he would have spent five years. The objective could be education, work assignment etc.

The first sentence sounds okay, but doesn't sound natural exactly. I would word it:

By the end of the year, I expect to have been to 5 countries.

This means that before the year gets over, you want to visit 5 different countries ( or so I assume).

And the second sentence:

I hope to visit Japan for several years.

I'm guessing this means that out of the 5 counties, you want one to be Japan.

These sentences are natural English.

１．I expect to have visited 5 countries by the end of the year.

２．I aim to stay in Japan for several years.

1. correct

2. I hope to be in Japan for several years.