nginx 'proxy_pass' cannot have URI part in location?

What's actually happening here?

nginx cannot process your desired URI part in the proxy_pass directive because you're within a named location (hence the error message). This is because nginx is built in a modular fashion and each configuration block is read in various stages by the various modules. So just remember that you cannot have a URI within your proxy_pass directive in the following cases:

1. Regular Expression Locations
2. Named Locations
3. if Blocks

How could we solve this problem?

Mohammad AbuShady explained how to do a rewrite and pass the requested URI to the proxy server. I just wanted to clarify the reason.

Technically just adding the URI should work, because it's documented here and it says that it should work, so

location @test{
    proxy_pass http://localhost:5000/1/; # with a trailing slash
}

Should have worked fine, but since you said it didn't I suggested the other way around, the trick is that instead of passing /my/uri to localhost:5000/1, we pass /1/my/uri to localhost:5000,

That's what my rewrite did

rewrite ^ /1$1

Meaning rewrite the whole URL, prepend it with /1 then add the remaining, the whole block becomes

location @test{
    rewrite ^ /1$1;
    proxy_pass http://localhost:5000;
}

Note: @Fleshgrinder provided an answer explaining why the first method didn't work.