Warlock spell progression is wholly distinct from the way every other spellcaster acquires additional spell slots. You can use the spell slots afforded by the warlock's Pact Magic feature to cast paladin spells (and vice versa), but they develop differently.
So, as a 5th-level paladin, you would have four 1st-level spell slots and two 2nd-level spell slots that recover after a Long Rest. You would also have two 2nd-level spell slots from Pact Magic that recover after a Short Rest. If you are also making use of the optional rules in Tasha's Cauldron of Everything, then you would also be able to use Harness Divine Power (p. 53) to recover one 2nd-level spell slot once per day; using your Channel Divinity.
However, and this cannot be stressed enough with multiclassing, you need to be careful. It can lead to powerful builds over the long term, but it can also leave you incapable of helping out. The warlock levels only give them access to 1 more spell to draw from, but those 5 spells are all 1st or 2nd-level. A 9th-level paladin has access to 3rd-level spells. A 9th-level warlock has access to 5th-level spells. Both grant access to additional features for their class and subclass. This means giving up the paladin's Aura of Protection and their 7th-level Sacred Oath feature. And it means giving up the warlock's 6th-level Otherworldly Patron feature along with three invocations.
What would my spell slots look like with this combo? I'm not sure.
Warlock spell progression is wholly distinct from the way every other spellcaster acquires additional spell slots. You can use the spell slots afforded by the warlock's Pact Magic feature to cast paladin spells (and vice versa), but they develop differently.
So, as a 5th-level paladin, you would have four 1st-level spell slots and two 2nd-level spell slots that recover after a Long Rest. You would also have two 2nd-level spell slots from Pact Magic that recover after a Short Rest. If you are also making use of the optional rules in Tasha's Cauldron of Everything, then you would also be able to use Harness Divine Power (p. 53) to recover one 2nd-level spell slot once per day; using your Channel Divinity.
However, and this cannot be stressed enough with multiclassing, you need to be careful. It can lead to powerful builds over the long term, but it can also leave you incapable of helping out. The warlock levels only give them access to 1 more spell to draw from, but those 5 spells are all 1st or 2nd-level. A 9th-level paladin has access to 3rd-level spells. A 9th-level warlock has access to 5th-level spells. Both grant access to additional features for their class and subclass. This means giving up the paladin's Aura of Protection and their 7th-level Sacred Oath feature. And it means giving up the warlock's 6th-level Otherworldly Patron feature along with three invocations.
Thank you, that helps a lot! I appreciate it!