And I currently should have 5 level 1 spell slots not 3.
No you shouldn't.
All classes contribute to the SAME singular ESL which determines spell slots.
At ESL 1 you will have 2 first level spell slots
At ESL 2 you will have 3 first level spell slots
At ESL 3 you will have 4 first level and 2 second level spell slots
At ESL 4 you will have 4 first level and 3 second level spell slots
At ESL 5 you will have 4 first level, 3 second level and 2 third level spell slots
At ESL 6 you will have 4 first level, 3 second level and 3 third level spell slots
At ESL 7 you will have 4 first level, 3 second level, 3 third level and 1 fourth level spell slots
At ESL 8 you will have 4 first level, 3 second level, 3 third level and 2 fourth level spell slots
At ESL 9 you will have 4 first level, 3 second level, 3 third level, 3 fourth level and 1 fifth level spell slots
At ESL 10 you will have 4 first level, 3 second level, 3 third level, 3 fourth level and 2 fifth level spell slots
At ESL 11 you will have 4 first level, 3 second level, 3 third level, 3 fourth level, 2 fifth level and 1 sixth level spell slots
At ESL 12 you will have 4 first level, 3 second level, 3 third level, 3 fourth level, 2 fifth level and 1 sixth level spell slots (Yes, the final attainable ESL in BG3 provides no additional spell slots)
This remains true irregardless of HOW you acquire these ESL.
Any combination of 1 level of Bard/Cleric/Druid/Sorcerer/Wizard, 2 levels of Paladin/Ranger or 3 levels of Eldritch Knight/Arcane Trickster will produce the same results at the same ESL.
This is different to prior editions where each class had their own unique ESL based on their specific class levels. Where you could get additional first level spell slots from getting an ESL in multiple classes. The upside to the new 5e version is you're now able to access higher level spell slots with multiclasses (And can upcast any known spell to any available spell level), at the cost of the number of first level spell slots you're able to obtain (And an overall decrease in total number of available spell slots, especially for Sorcerers)