My friends are in a campaign right now, and I made a druid. When we were leveling him up to level 5 like the other PCs, we just gave him however many spells he had spell slots of, which just doesn't seem correct. Other classes, like the bard, ranger, and sorcerer, specifically say how many spells they know at what levels. The druid only says how many cantrips are known, how many spell slots they have, and how many spells they can prepare. How do I determine how many spells my druid knows?
Your level 5 druid knows all spells on the Druid Spell list ...
... from levels 1, 2 and 3.
The problem you have is: which ones does the druid prepare on a given day?
How to translate the rules?
You have to make choices after each long rest to either
keep prepared the ones you had the day before, or
prepare a different set.
This makes playing a druid (and a cleric) require a little more thought, and some forecasting, to try and have the right spells prepared for a given adventure.
Preparing and Casting Spells
You prepare the list of druid spells that are available for you to cast, choosing from the druid spell list.
When you do so, choose a number of druid spells equal to your Wisdom modifier + your druid level (minimum of one spell). The spells must be of a level for which you have spell slots.
Let's assume a Wisdom score of 18 for a 5th level druid. You can prepare nine spells. You have to choose a combination of 1st, 2nd, and 3rd-level spells that equals 9. For example, pick 7 firsts and a second and a third, or 6 seconds and two firsts and a third, and so on. You can still only cast them with the spell slots you have: 4 first-level slots, 3 second-levels, and 2 third-levels.
You can also change your list of prepared spells when you finish a long rest. Preparing a new list of druid spells requires time spent in prayer and meditation: at least 1 minute per spell level for each spell on your list.
Choose what you think will help your party the best.