Interesting question but since some details are unclear but really relevant i'll try to add some reasonable inputs.
The earth surface is 5x10^14[m^2], 70% of the earth surface is water, then we have 1.5 x 10^14 [m^2] of dry surface.
If you distribute evenly your 5K humans on the sruface you will have 0,0000333 human/Km^2, that equals 30K [Km^2] for every person. That's a lot, not only the mating chanches but also the meeting chanches are way too low to reasonably think to form a critical mass and (re)start a civilization.
In this hypotesis everyone could reasonably think to be the last man on the world, therefore i'll assume that your 5K are somehow grouped. On the other hand 5K people in one group are a lot of people to manage, without our civilization, and in this case i expect that most of them will die because internal rather than external issues.
As a natural/common rule for non apex predators, safety is in numbers but at the same time overpopulating an area will could be way more dangerous than living in a sub-optimal population number: the population could be decimated by starvation and the local food chain could be crippled enough to require a migration to avoid extinction.
I would choose a 2-300 people as ideal group dimension, considering that 1/3 will die soon meanwhile the others will (try to) settle.
I'd also remove at least the "no belongings" requirement, otherwise tbh it's a no chanche situation except for really (few) trained people.
I'm not saying that they should have a lot of technologically advanced tools, or fuel, etc, but if you think that someone can be thrown back in the wilderness -without anything- the place should be at least really comfortable.
There are some youtube channels in which a guy uses his bare hands to build some tools, a hut, a stove, fishing traps, etc, with only primitive technologies.
Even though this is feasible it requires time and, except in the case a group is so lucky to begin the new civ during spring in some awesome places full of fruit trees and small river, this required time is a huge reduction of survival chanches. If a group happens to begin during winter on a mountain or during summer in the savannah, i doubt that there's any chances for them to survive. They will need calories from the very first moment and, depending on the climate, probably a shelter from day one.
Moreover, even if someone is capable to grow vegetables since day 1, the harvesting season could be months later (not to mention fruit trees that needs way more to produce something). Consider also that a really good source of proteins and other nutrients could be chickens, they convert pretty much everthing that's organic in meat and eggs, but where are you supposed to find selected breeds of broilers in the wilderness? Is not that useful to be a trained farmer if you don't have time to grow anything and raise animals before starvation...
A medic wihtout an hospital and medicines is not very useful, but it would be way less useful witout his bag. Even with only a scalpel and stethoscope his efficiency is significantly rased.
My suggestion is to give these people at least few things, like a small backpack full of their related things, for example:
medic bag for a medic with scalpel, stethoscope, few pills and some bandages,
few type of seeds for farmer B,
few chicken for farmer A,
binoculars and a knife for some people (example: athletes),
a couple of pans and a kitchen knife for some people (example: someone who knows how to cook),
an handsaw and chisel for the woodworker,
fishing pole for fishermen (useful at least at the beginning) and so on.
I think that even with these benefits it won't be easy, at all, because they don't just have to survive a couple of weeks, they are supposed to start a new civ, and this means that they have to organize themselves, build a reliable (food) economy without destroying the surrounding environment, build shelters, build tools, create clothes (other ones, you have to live a really different life) and especially survive the winter.
With that being said, there are few other things that needs to be accomplished:
- you need to designate a wise, strong leader soon,
you have nominate rational people to organize the tasks prioriest and best practicies (where to build the settlement, prioritize shelter building or food gathering, etc),
you have to allocate the skilled people as a team leader for the tasks (farmers, wood workers, etc),
you have to convince the non skilled people to do what has to be done (musicians, webdesigner, truck driver, insurant agent, anything that's not useful to survive in the wilderness), and to do that you need a strong leader and the this complete the circle.
Please note: this is anything but easy or likely to happen!
Tl,dr: a determined, united and cooperative group of 2-300 people with few tools/seeds/chicken could have a reasonable chance not to die within the first winter IF they start in a very cofortable area.
If we pick random people with no tools, from different zones, with different cultures and with different languages the best case scenario is to have someting more similar to "the waliking dead" for a while and then nothing than a new civilization.
Once (and especially if) said group survived some years, the settlement should be done and a real grow in numbers can happen. After few decades the original population is adapted and they are living their "normal" life, with their offspring, maybe getting in touch with other groups to start trades.
Hopefully at least few wise and erudite people were capable to preserve knowledge about the most relevant topics, therefore you will have a really tiny human density (respect to the current density) with a huge amount of resources per person and the knowledge on how to take advantage of them.
If no cataclysm happen, then a fast population grow will eventually happen and the world repopulation is down the road.
Would it take many millennia to develop the technology all over again?
It depends on how capable they are to preserve knowledge, but probably millennia are not required.
Paper is not that hard to produce, and the wise ones can write at least the most relevant sceintific discoveries known so far. You won't have "big pharma" anytime soon, but the knowlege that from pennicillium mould you can produce antibiotics is priceless. You don't have to reinvent the wheel, the crop rotation, the selective breeding, the nitrogen/phosporus/potassium fertilizer, the steam motor, the mechanical press printing, the gunpowder, the stainless steel alloy, darwinian theory, classical mechanic, battery chemistry, polymers, the airfoil (not only for the planes, also for the sails), the electrical motor, the atom structure the chemical bonds and the periodic table. Even if you can't preserve the knowledges that are behind a theory, the pratical meaning is still useful and even the bare final concept (as simple as "gravity acceleration is the same for every object") will be a priceless hint for the future scientists.
Or less time because we have knowledge about them?
Definitely less time.
Would we even be alive to see the day?
Definitely no, it will need generations in the best case scenario.
Scientists are a really specialized human beings, and this specialization requires a lot of supports from a lot of other supporting technical people. And a lot of technical people, well, requires A LOT of people that take care of food, safety, etc... Starting from scratch, you have to stabilize the first human pool, then grow in number, then develop technicians, and then scientists (a quantum physicist without our technology and engineers is only a philosopher).