5 days to carb, Best method???

I have 5 days to carb my beer after it being in the primary for 3 weeks and then it will be sitting in the keg for a week(Off topic question, when its sitting in the keg for a week what temperature should it be at??). My question is what would be the best method for caring the beer if i only have 5 days to when i want to drink it?
Thanks in advance for all your help.

If possible get it cold and rack it to the keg, or rack it to the keg and then get it cold. Hit it with 30 PSI for a second and then vent that through the pressure relief valve to get rid of any oxygen. After that you'll want to put the gas disconnect back on it at 30 PSI and shake it for a couple minutes (I roll it back and forth on my legs as I sit). Then set it upright and relieve the pressure again. Dial the pressure down to 12 PSI and put the disconnect back on and you should be pretty close to your carb level. You'll want to keep it cool at 12 psi for it to carb up the rest of the day, should be perfect by the next day, drinkable immediately though.

I'd keep the keg at around 40 for storage/carbing but it can depend on style.

Plenty of time! Crash cool if possible before racking to keg, cooler beer absorbs CO2 faster. Rack to keg, hit it with 30psi for 3 days. This will overcarb just a bit, but will not be fully carbed. Lower the pressure down to 8psi and let sit for the remaining 2 days.

If it were me I would chill it in the keg immediately. Set the PSI to 30 (purge the O2) and let the keg sit for 48 hours. At the end of 48 hours, dial down the PSI, bleed the excess pressure and set to serving PSI and taste. It should be adequately carbonated by that point.

Depending on the style...you may want to shorten the time a bit. English Ales taste much better with less carbonation.

The only reason I don't advocate shaking anymore is since you (apparently) are serving this to guests...the 5 full days of chilling and sitting still will lead to clearer beer.

If you beer is already chilled when you hook up the gas...drop the time down to 36 hours (cold beer absorbs CO2 much quicker than warm).

You might also want to blend in a tablespoon of dissolved (unflavored) gelatin to speed the settling/clearing process.