From Articles I–VII of the US Constitution, what are five examples of violations of popular sovereignty, political equality, political liberty, justice and/or democracy?

Breaches of the 1st Amendment would include the following: 
The government adopting a national religion
The government forcing you to practice a religion 
The government preventing you from practicing your religion of choice, so long as no one is being injured and no laws are being violated
The government preventing you from speaking your mind, so long as it isn't endangering those around you
The government preventing you from peacefully assembling
Breaches of the 3rd Amendment would include the following: 
The government, through an act of Congress or Executive action, mandating that you must allow soldiers to occupy your residence and feed them
Breaches of the 4th Amendment would include the following:
The government (i.e. representatives of the government, police, etc.) taking your property or rummaging through your personal belongings without probable cause
The government (i.e. representatives of the government, police, etc.) detaining you for no reason
Breaches of the 5th Amendment would include the following:
The government making you give testimony that would hurt your own defense in a legal case
The government retrying you for a case where you've already been found innocent
The government taking your things without going through a legal process to do so
The government taking your things for public use without compensating you for the seizure
https://www.law.cornell.edu/constitution/first_amendment