A major disadvantage would be a greatly increased risk of resource depletion. Another would be the risks faced by these creatures before they can reproduce.

At its core, the purpose of life is to ensure the continuation of the species. Life begets life. Hence, if you want a species to have an exceptionally long life span, then there should be something about that longer lifespan which has, on evolutionary timescales (which work on generations, not years), helped ensure the survival of the species, and ideally an individual's own offspring. In evolutionary terms, parents' responsibility to help safeguard the survival of their offspring lasts until their offspring has matured to the point of having offspring of their own. We see this pattern time and again in nature, particularly in species that have fewer offspring but tend to them: offspring leaves their parents once they are near or at sexual maturity, not before.

Every individual who is alive, including those who are unable (too young, too old, sick or infirm) to defend themselves and to reproduce, requires sustenance. You mention medicine, but that's the last thing you should be concerned about, because frankly, especially with the technology level you seem to have in mind, keeping sick and infirm individuals alive would be a luxury, not something to be taken for granted. If their technology level is "around medieval level", they are going to have serious challenges growing or catching sufficient food. Each individual will require, irrespective of their preferred food source, far more biomass to sustain themselves for 5,000 years than for 50 years. This presents a number of challenges especially because in the era you are comparing against, life for the vast majority of humans was already at a sustenance level. Particularly if combined with a greatly reduced birth rate, you will have far more individuals who are at a stage of their life where they are not reproducing or tending to offspring and thus, from an evolutionary perspective, are not productive members of their species.

You can in principle do something like make their life cycle such that they don't reproduce until age 3,000 years, but then you have to explain how they got to that point. What was the advantage to having one's first offspring, on average, at age 3,000 years instead of at age 3 years or 30 years? Every year you add to the age when they have offspring is a year that comes with the risk of debilitating injuries, famine, perhaps war. Parents who get offspring that reproduce later would have a greater risk of not having any great-offspring. If anything, there would seem to be an evolutionary pressure to reproduce earlier rather than later, but there is a natural limit to how early it is reasonable for a complex organism to reproduce. In order to as much as maintain a population size, on average, each pair needs to have two offspring who survive long enough to have offspring of their own.

A major disadvantage would be a greatly increased risk of resource depletion. Another would be the risks faced by these creatures before they can reproduce.

At its core, the purpose of life is to ensure the continuation of the species. Life begets life. Hence, if you want a species to have an exceptionally long life span, then there should be something about that longer lifespan which has, on evolutionary timescales (which work on generations, not years), helped ensure the survival of the species, and ideally an individual's own offspring. In evolutionary terms, parents' responsibility to help safeguard the survival of their offspring lasts until their offspring has matured to the point of having offspring of their own. We see this pattern time and again in nature, particularly in species that have fewer offspring but tend to them: offspring leaves their parents once they are near or at sexual maturity, not before.

Every individual who is alive, including those who are unable (too young, too old, sick or infirm) to defend themselves and to reproduce, requires sustenance. You mention medicine, but that's the last thing you should be concerned about, because frankly, especially with the technology level you seem to have in mind, keeping sick and infirm individuals alive would be a luxury, not something to be taken for granted. If their technology level is "around medieval level", they are going to have serious challenges growing or catching sufficient food. Each individual will require, irrespective of their preferred food source, far more biomass to sustain themselves for 5,000 years than for 50 years. This presents a number of challenges especially because in the era you are comparing against, life for the vast majority of humans was already at a sustenance level. Particularly if combined with a greatly reduced birth rate, you will have far more individuals who are at a stage of their life where they are not reproducing or tending to offspring and thus, from an evolutionary perspective, are not productive members of their species.

You can in principle do something like make their life cycle such that they don't reproduce until age 3,000 years, but then you have to explain how they got to that point. What was the advantage to having one's first offspring, on average, at age 3,000 years instead of at age 3 years or 30 years? Every year you add to the age when they have offspring is a year that comes with the risk of debilitating injuries, illness, famine, perhaps war. Parents who get offspring that reproduce later would have a greater risk of not having any great-offspring. If anything, there would seem to be an evolutionary pressure to reproduce earlier rather than later, but there is a natural limit to how early it is reasonable for a complex organism to reproduce. In order to as much as maintain a population size, on average, each pair needs to have two offspring who survive long enough to have offspring of their own.