Exception

Acredito que o erro está no arquivo persistence.xml. Você baixou ele?

Não baixei mas copiei igual

Cole ele aqui, por favor.

<persistence xmlns="http://java.sun.com/xml/ns/persistence"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://java.sun.com/xml/ns/persistence
        http://java.sun.com/xml/ns/persistence/persistence_2_0.xsd"
    version="2.0">

    <!-- unidade de persistencia com o nome financas -->
    <persistence-unit name="financas">

        <!-- Implementação do JPA, no nosso caso Hibernate -->
        <provider>org.hibernate.jpa.HibernatePersistenceProvider</provider>

        <!-- Aqui são listadas todas as entidades -->
        <class>me.mauro.hibernate.Conta</class>

        <properties>    
            <!-- Propriedades JDBC -->
            <property name="javax.persistence.jdbc.driver" 
                value="com.mysql.jdbc.Driver" />

            <property name="javax.persistence.jdbc.url" 
                value="jdbc:mysql://localhost/financas" />

            <property name="javax.persistence.jdbc.user" value="root" />
            <property name="javax.persistence.jdbc.password" value="" />

            <!-- Configurações específicas do Hibernate -->
            <property name="hibernate.dialect" 
                value="org.hibernate.dialect.MySQL5InnoDBDialect" />

            <property name="hibernate.hbm2ddl.auto" value="update" />
            <property name="hibernate.show_sql" value="true" />
            <property name="hibernate.format_sql" value="true" />
        </properties>
    </persistence-unit>
</persistence>

Você adicionou todas as dependências?

Penso que sim, tem aqui uma foto https://imgur.com/a/uDJAxuk

Tente trocar <provider>org.hibernate.jpa.HibernatePersistenceProvider</provider> por <provider>org.hibernate.ejb.HibernatePersistence</provider>

Obrigado, penso que funcionou, mas desencadeou outro erro:

java.sql.SQLException: Unknown initial character set index '255' received from server. Initial client character set can be forced via the 'characterEncoding' property.
    at com.mysql.jdbc.SQLError.createSQLException(SQLError.java:1055)
    at com.mysql.jdbc.SQLError.createSQLException(SQLError.java:956)
    at com.mysql.jdbc.SQLError.createSQLException(SQLError.java:926)
    at com.mysql.jdbc.ConnectionImpl.configureClientCharacterSet(ConnectionImpl.java:1689)
    at com.mysql.jdbc.ConnectionImpl.initializePropsFromServer(ConnectionImpl.java:3444)
    at com.mysql.jdbc.ConnectionImpl.createNewIO(ConnectionImpl.java:2062)
    at com.mysql.jdbc.ConnectionImpl.<init>(ConnectionImpl.java:723)
    at com.mysql.jdbc.JDBC4Connection.<init>(JDBC4Connection.java:46)
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)
    at java.base/jdk.internal.reflect.NativeConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/jdk.internal.reflect.DelegatingConstructorAccessorImpl.newInstance(Unknown Source)
    at java.base/java.lang.reflect.Constructor.newInstance(Unknown Source)
    at com.mysql.jdbc.Util.handleNewInstance(Util.java:406)
    at com.mysql.jdbc.ConnectionImpl.getInstance(ConnectionImpl.java:302)
    at com.mysql.jdbc.NonRegisteringDriver.connect(NonRegisteringDriver.java:282)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at org.hibernate.service.jdbc.connections.internal.DriverManagerConnectionProviderImpl.getConnection(DriverManagerConnectionProviderImpl.java:193)
    at org.hibernate.tool.hbm2ddl.SuppliedConnectionProviderConnectionHelper.prepare(SuppliedConnectionProviderConnectionHelper.java:51)
    at org.hibernate.tool.hbm2ddl.SchemaUpdate.execute(SchemaUpdate.java:194)
    at org.hibernate.tool.hbm2ddl.SchemaUpdate.execute(SchemaUpdate.java:178)
    at org.hibernate.internal.SessionFactoryImpl.<init>(SessionFactoryImpl.java:503)
    at org.hibernate.cfg.Configuration.buildSessionFactory(Configuration.java:1750)
    at org.hibernate.ejb.EntityManagerFactoryImpl.<init>(EntityManagerFactoryImpl.java:94)
    at org.hibernate.ejb.Ejb3Configuration.buildEntityManagerFactory(Ejb3Configuration.java:905)
    at org.hibernate.ejb.Ejb3Configuration.buildEntityManagerFactory(Ejb3Configuration.java:890)
    at org.hibernate.ejb.HibernatePersistence.createEntityManagerFactory(HibernatePersistence.java:57)
    at javax.persistence.Persistence.createEntityManagerFactory(Persistence.java:63)
    at javax.persistence.Persistence.createEntityManagerFactory(Persistence.java:47)
    at me.mauro.hibernate.Main.main(Main.java:16)

Esse erro aparece 3 vezes

Baixe a nova versão do MySQL Connector.

Atualizei e agora recebo esse erro

Exception in thread "main" java.sql.SQLException: Access denied for user ''@'localhost' (using password: NO)
    at com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:129)
    at com.mysql.cj.jdbc.exceptions.SQLError.createSQLException(SQLError.java:97)
    at com.mysql.cj.jdbc.exceptions.SQLExceptionsMapping.translateException(SQLExceptionsMapping.java:122)
    at com.mysql.cj.jdbc.ConnectionImpl.createNewIO(ConnectionImpl.java:835)
    at com.mysql.cj.jdbc.ConnectionImpl.<init>(ConnectionImpl.java:455)
    at com.mysql.cj.jdbc.ConnectionImpl.getInstance(ConnectionImpl.java:240)
    at com.mysql.cj.jdbc.NonRegisteringDriver.connect(NonRegisteringDriver.java:207)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at java.sql/java.sql.DriverManager.getConnection(Unknown Source)
    at com.mysql.cj.jdbc.admin.TimezoneDump.main(TimezoneDump.java:70)

Meu persistence.xml: https://hastebin.com/ufewugasul.xml (Você precisa trocar o <class> apenas)Versões:MySQL: 8.0.13Hibernate-Core: 5.3.7.Final

Se puder, teste com essas configurações acima. Aqui funcionou normal.

Exception in thread "main" org.hibernate.service.spi.ServiceException: Unable to create requested service [org.hibernate.engine.jdbc.env.spi.JdbcEnvironment]
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.createService(AbstractServiceRegistryImpl.java:275)
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.initializeService(AbstractServiceRegistryImpl.java:237)
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.getService(AbstractServiceRegistryImpl.java:214)
    at org.hibernate.id.factory.internal.DefaultIdentifierGeneratorFactory.injectServices(DefaultIdentifierGeneratorFactory.java:152)
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.injectDependencies(AbstractServiceRegistryImpl.java:286)
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.initializeService(AbstractServiceRegistryImpl.java:243)
    at org.hibernate.service.internal.AbstractServiceRegistryImpl.getService(AbstractServiceRegistryImpl.java:214)
    at org.hibernate.boot.internal.InFlightMetadataCollectorImpl.<init>(InFlightMetadataCollectorImpl.java:179)
    at org.hibernate.boot.model.process.spi.MetadataBuildingProcess.complete(MetadataBuildingProcess.java:119)
    at org.hibernate.jpa.boot.internal.EntityManagerFactoryBuilderImpl.metadata(EntityManagerFactoryBuilderImpl.java:904)
    at org.hibernate.jpa.boot.internal.EntityManagerFactoryBuilderImpl.build(EntityManagerFactoryBuilderImpl.java:935)
    at org.hibernate.jpa.HibernatePersistenceProvider.createEntityManagerFactory(HibernatePersistenceProvider.java:56)
    at javax.persistence.Persistence.createEntityManagerFactory(Persistence.java:79)
    at javax.persistence.Persistence.createEntityManagerFactory(Persistence.java:54)
    at me.mauro.hibernate.Main.main(Main.java:16)

Recebo esse erro

Esse é o erro completo? Não tem algo mais abaixo dele?

Sim, aparece mais, mas já resolvi. Acho que eram as versoes do mysql connector e do hibernate que não eram compativeis ou assim... Usei respectivamente as versões 8.0.12 e 4.3.3