How do cooking utensils remain safe for use

I can't see any reason for the marinating itself to make any difference. If it's safe to leave the (un-marinated) meat in the same conditions for the same length of time, then it's safe to marinate it for that long.

Five days in the refrigerator is definitely stretching it for chicken - usually no more than a few days is recommended, and that's assuming it was fresh when you bought it (not a day before the sell-by date). Even if it's safe, it's not going to be very good. I've accidentally left raw chicken in the refrigerator and forgotten about it before, and it started to smell "off" after about 4 days. I hate to say it, but I wouldn't use it at this point.

As for the steak, you're probably okay, because you only have surface bacteria, but I would cook it well and right away. Again, most cooks I know will recommend no more than a few days in the fridge.

P.S. I've heard people say that weak acids such as lime juice "preserve" the meat, but never from a reliable source; even if it worked, every marinade is different and it would be nearly impossible to predict the exact amount of time it preserves for. You have no idea how much bacteria existed at the outset, and even if the marinade somehow helped to inhibit growth of new bacteria, the "spoiled-ness" of raw meat doesn't come from the bacteria itself but from the toxins they leave behind. It's not a requirement for the bacteria to multiply in order for the food to spoil, if enough existed in the first place.

Unless somebody has it on good authority that marinating makes any significant difference, I refuse to put any stock in that bit of folk wisdom and recommend that others be equally skeptical.

It depends on where you live. Each country has different meat diseases and bacterium that you have to be careful about

Traditionally in many western countries most meats are relatively safe raw though poultry is often not. But the definition of safe is not universal. Fresh chicken may have some salmonella etc, but unless this is allowed to grow to large numbers of spore it will not be dangerous. There are some bacteria that are dangerous in even minute amounts, but these should be vary rare, and even the cleanest cook will probably still transfer them

So to answer question, when cooking meat (or anything for that matter), you have to consider the amount of food adhering to the utensil, and the time it is exposed to a temperature in which bacteria can grow etc

If there was a formulae it would be something like

food type (risk of bacteria) * temperature * time

In general ground meat has been processed but not overly preserved, so time starts becoming a factor. How long has it been in a warm environment? Bacon is heavily preserved and not a great bacteria home, so you have more time before it becomes a risk. I small smear of bacon juice on a fork is not going to create a dangerous level of bacteria in the 20 minutes it takes you to cook the dish. But I wouldn't risk it for Chicken (in my country due to campylobacter still being a problem)

In the home environment I give anything that has touched raw food a quick rinse under the tap (Which just happens to be collected rain water and therefore full of bird poo :-) ) and sometimes a mechanical scrub with the dishes brush before using it again in the cooking process

There are lots of old wives tales on kitchen cleanliness, but the end result is that bacteria needs water, food, and temperature to grow. If you remove most of these they can't multiple to dangerous levels

From my experience in food technology laboratories, the often overlooked problem is surface oil and fat. These trap water, food and bacteria (the perfect storm). Simple mechanical scrubbing will remove vast amounts of these for short term (period of cooking) cleanliness

This of course does not apply to food that must be cooked for non bacterial reasons, and food known to be unclean. Chicken again is typical of this, and I would hot water scrub everything used with raw or partially cooked chicken