A successful DC 10 Wisdom (Medicine) check will stabilize a dying creature.
The rules for stabilizing a creature state:
You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check.
A stable creature doesn’t make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making death saving throws again, if it takes any damage. A stable creature that isn’t healed regains 1 hit point after 1d4 hours.
Note, stabilizing a creature this way does not bring them to consciousness. They just stop dying. With a +5 to your Medicine skill, a die roll of 5 or more would have succeeded under the official rules.
Further, you can use a Healer’s Kit that makes this even easier:
Healer’s Kit. This kit is a leather pouch containing bandages, salves, and splints. The kit has ten uses. As an action, you can expend one use of the kit to stabilize a creature that has 0 hit points, without needing to make a Wisdom (Medicine) check.
Healer’s Kit is listed under “Other Adventuring Gear” in the Player’s Handbook (pg. 151) and only costs 5 gp. It eliminates the need to make any checks.
It seems likely that your DM is using a house rule for this. Personally, you not knowing about a house rule is a bit of a red flag. You should take the time to talk to the DM about other house rules they are using. Everyone needs to know the rules of the game. The rules are the primary tool the players have for managing expectations about the decisions they make, I write about this in this answer:
If I know my DM is going to apply the rules as written with a reasonable measure of consistency, I am equipped to think through the space of outcomes my actions might have - I am aware of all the possible rules that may apply, and what different outcomes might look like when I roll the dice. But if I know my DM is consistently inconsistent in their rulings, every situation becomes a two way lottery: I gamble on the whims of the DM, and the DM gambles on the players coming up with reasonable or unreasonable ideas.
Not knowing what rules are going to apply in a particular situation is a recipe for hurt feelings and disappointment.
