Note that the $5676 is before taxes. So if you add taxes to that, then rent becomes about 50% of the income.
Also note, that raising min-wage for you, also means raising it for the staff that maintains your apartment, and for the staff at the utility companies, and the grocers, and the delivery staff, etc. Which means that all cost of living goes up to pay the higher wages.
It will cost more to bring in your groceries, to bring in the gas for your car, for the upkeep of the apartment that you are renting.
After the min wage increase, you will be able to afford less and have a higher chance of being laid off from your job when your employer cannot afford to pay you from the loss of business.
The real solution is to kill all taxes. And remove all regulations from people providing housing competition. Competition always brings down prices.
The proof is in the foodservice industry. Who makes more money per day, the high volume moderate-quality fast food joint, or the high-quality expensive restaurants? The number of eatery closures each year points out the answer every year, and every year people ignore that answer.
This is also why our data plans for the internet are so expensive. Most cities only allow one major cable or fiber owner into a city, which then all providers are reselling that one data service. That is a monopoly with a thin veneer of the appearance of a free-market.
Why are cell data plans so expensive? More anti-trust activities, as controlled by the FCC. FCC limits cell towers in a region, creating a defacto monopoly or duopoly. All other services sold in that region are required to resell the tower services of the non-competitive owners of the towers.
One cannot have a monopoly or duopoly without the threat of violence. In the long past, this was armed thugs or blatant armed tax collectors for the crown enforcing the collections. These days extra steps have been added called regulatory industry, which then sends their lawyers first, then they will contract with law enforcement, all to violate your voluntary interaction with a business or individual of your choice.
The solution isn’t minimum wage, it is the removal of government from business, and a well-armed citizenry.