In Shadowrun 5th Edition, there is no Spirit Pact quality (research seems to indicate there was one for SR4). Is there anything in the rules that would explicitly prevent an SR5 character from starting with a Spirit Pact?
By RAW, you can't because there isn't a written rule that says you can. Spirit Pact has mechanical benefits, and there's no explicit way for a starting character to pay for them. They're meant to be gained in play, via in-character negotiation with powerful magical entities.
If you want to go beyond RAW, many of the Spirit Pacts are very powerful. You could look at the benefits and drawbacks of each pact and derive a cost. It's easiest if you're using Point Buy (Run Faster, p.64) because that gives you a single currency (Karma) to buy everything with, even things that normally take money.
Drain Pact is probably the easiest to adjudicate. It's vaguely similar to a Spellcasting Spell Focus (SR5, p.320) in that it grants bonus dice (albeit to Drain Resistance Tests rather than Spellcasting), but for all five types of spells. You could charge this one at the cost of all five Spellcasting Spell Focuses of a rating that matches the dice the spirit imparts. The character can't be deprived of it by any means other than the providing spirit, so it should be somewhat more expensive. However, in light of the included addiction, I wouldn't charge more (I wouldn't give back points for the Addiction, though.)
Dream Pact is depends on what the spirit does with the character's body when he's asleep. This particular pact doesn't really have any advantages for the character, only the spirit. You could model it with a variety of flaws, just with different reasons for having them:
- Bad Rep if the spirit does things, and the character takes the blame.
- Dependents if the spirit leads a life with your body, but they come at you for things like child support.
- Insomnia if the character realizes he made a deal he can't get out of, and tries to avoid sleep to avoid the spirit taking control.
- Spirit Bane if the spirit is using his body to somehow take action against other types of spirits.
...and that just covers the ones in SR5. Run Faster and other sourcebooks have others that may be appropriate.
Formula Pact is almost impossible to put a point value to. It has a very powerful benefit to the human (Immunity to Age). Combined with a Spirit Pact making both die (spirit and human) if either dies, the spirit has very strong motivation to watch out for the character. As a Formula Pact insulates a spirit from other uses of it's Spirit Formula, a Free Spirit likely make this pact as a defense against some other person or group that controlled it in the past. A Formula Pact is the focus of an entire campaign, not just a single character - all the player characters will get caught up in the backlash and blast radius of such a complication.
Life Pact is equally difficult to adjudicate. It is very powerful, and has no drawback for the spirit. The ability to directly spend Karma on healing (whatever the rate) eliminates much of the threat of combat.
Magic Pact is a bit more of a fair exchange for the spirit. Mechanically, it's very similar to a Power Focus, though it doesn't last nearly as long. How much it's worth depends on the GM; if the group gets hit with multiple heavy combat encounters in the same day, it's worth less. If it's only likely to be triggered once a day, it's worth more than a Power Focus, because it can't be lost, stolen, or misplaced. However you gauge the base cost, it should be reduced because the spirit can use up the human's Edge.
Power Pact is transitory, it only lasts 24 hours and has to be reactivated. I wouldn't even bother trying to establish a character-creation equivalency.
No matter how you adjudicate the magical abilities the spirit gives you, they absolutely must be taken as a Contact (SR5, p.98 and p.386). Free Spirits are powerful, so even if they don't have a lot of human connections, they should still have a high Connection rating. The nature of the relationship determines the Loyalty, as always.