Magic 5 -> 6 = 18
Magic 6 -> 7 = 21
Grade 0 -> 1 = 13
Grade 1-> 2 = 16
To raise your magic from 5 to 7 will require 39 karma. To initiate twice, you're looking at another 29 karma. That's a total of 68 karma. That seems like quite alot, and it is. If your GM tends to give out something in the area of 4 karma a run, that'll be 17 jobs you have to do. If he gives out 5, then that drops down to about 14 (rounded up.)
Advancement as an awakened character takes quite a long time, but then I see them as slow growers anyway. Adepts really have it hard, because while a magician can just learn another spell or conjure a spirit to aid him with his tasks, an adept more or less relies purely on the powers they get from their PPs.
Consider floating past your GM the optional rule in Street Magic (I believe) where an adept who initiates can choose to take another Power Point instead of a metamagic. That might alleviate some of your karma problems, though you'll be missing out on some of the really decent metamagics (Adept Centering is sweet, in my opinion.) However, it typically costs alot less to initiate than to buy up your magic rating, so you can revisit the initiation thing alot quicker than you can amass the karma to raise your Magic rating.
If you really want to take advantage of some karma savings, consider investing 4 karma (if you haven't already) into learning a rank in Arcana so you can join a magical group. If you go through the process of joining (which will require 5 karma along the way) then you can have up to a 40% reduction in your karma costs for initiation, assuming you let them help you with an Ordeal on your initiation.
I hope some of these ideas help.