You need a shimano splined bb tool like this to remove the old one:
Drivetrain side is LH thread, NDS is RH, so opposite to your pedals.
You will need a new tool to fit an Hollowtech2 external bearing bb such as the 105 one you mentioned.
Mostly its a spanner, but sockets are available.
The crankarms and axle are as 1, so all it does is slide through the bearings, and any end float is taken out like an aheadset.
Edit: just reading back, how old is your rear wheel? If its the same vintage as the rest of the bike, then an 11spd cassette is very unlikely to fit....
Drivetrain side is LH thread, NDS is RH, so opposite to your pedals.
You will need a new tool to fit an Hollowtech2 external bearing bb such as the 105 one you mentioned.
Mostly its a spanner, but sockets are available.
The crankarms and axle are as 1, so all it does is slide through the bearings, and any end float is taken out like an aheadset.
Edit: just reading back, how old is your rear wheel? If its the same vintage as the rest of the bike, then an 11spd cassette is very unlikely to fit....