#### Answer

(a) The temperature change of the paint would be $10.75~K$
(b) The amount of heat that flowed to the surroundings is $55,650~J$

#### Work Step by Step

(a) We can find the work done on the system in 5.00 min:
$W = P~t = (448~W)(300~s) = 134,400~J$
We can find the temperature change:
$\Delta T = \frac{134,400~J}{12,500~J/K} = 10.75~K$
The temperature change of the paint would be $10.75~K$
(b) We can find the change in internal energy of the paint:
$\Delta U = (12,500~J/K)(6.3~K) = 78,750~J$
We can find the amount of heat that flowed to the surroundings:
$Q = 134,400~J-78,750~J = 55,650~J$
The amount of heat that flowed to the surroundings is $55,650~J$