No, you can't cast it using a spell slot.

Spells you can cast because of your race aren't spells you know, and thus can't be spells you prepare. Per the PHB (p. 201, "Known and Prepared Spells"):

Before a spellcaster can use a spell, he or she must have the spell firmly fixed in mind ...

... and it goes on to describe some of the class-specific variations of knowing and preparing spells. But in any case, having a feature from your race or class that allows you to cast a spell isn't the same as knowing the spell.

This is spelled out clearly in the multiclassing rules for Pact Magic quoted in the question (PHB p. 164; emphasis mine).

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.

Likewise, the Drow Magic trait clearly distinguishes the known cantrip from the merely castable other spells (PHB, p. 24; bold for emphasis mine):

You know the dancing lights cantrip. When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting ability for these spells.

If the intent of the rules was that Drow also knew the non-cantrip spells, it would say so.

Nothing in the standard rules seems to forbid it.

Flexible casting allows you to create spell slots:

You can transform unexpended sorcery points into one spell slot as a bonus action on your turn.

These slots are treated no differently to the rules than normal spell slots.

The rules for learning spells say:

Each of these spells [you learn] must be a level for which you have spell slots.

Since you have a 5th level slot, by a strict reading you could do this.

There are no other rules¹ that I can find or think of that have any effect on the ability to do this, thus it seems to be permissible (or at least not explicitly excluded) by the rules.

It may not work depending on how the DM does leveling

There are no normal rules about when level up occurs, but many DMs allow leveling at the end of a long rest.

Since created spell slots vanish when you long rest, they would be gone before you could level and choose your spell.

Any spell slot you create with [Flexible Casting] vanishes when you finish a long rest.

If your table levels after a long rest, then this strategy won't work.

Almost certainly not intended (or at least planned for)

This is clearly a loophole use of the ability and is almost certainly not intended to work this way.

For example the following sentence of the rules about learning new spells says:

For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level.

This is referring to the spellcasting table for Sorcerer which outlines the slots a Sorcerer has at each level (and number of spells known). Note that there is no qualification here (eg "...unless some other feature grants you more slots"). The implication in the rules, though it is not explicitly stated, is that when the rules say "level for which you have slots" they mean "level for which you have slots according to the table".

Probably not worth it

A DM can certainly allow this and I don't think it would destroy their game alone (though I have not and likely will not ever play with this ruling). The exploit only seems to exist for 5th level spells so the impact, at least, is contained to that alone. In the end the sorcerer is trading almost all of their sorcery points just for the chance to cast up to two 5th level spells one level earlier. Even so, I would think hard before allowing it unless you think this will enhance the fun at your table.