We can separate this solid into two pieces: a cylinder and a cone. I will be finding the surface area's separately, then adding them together in the end.
Cylinder: The formula for the surface area of a cylinder is 2πrh+2πr². HOWEVER, since the cone and cylinder are connected, they don't count as part of the surface area, we don't need the 2 in 2πr². The radius, or r, is 5 cm. The height, or h, is 12 cm. Then, we use those numbers and plug it in the formula.
2πrh+πr²
2π(5)(12)+π(5)²
120π+25π
145π cm²
Cone: The surface area of the cone without its base is πrL where r is the radius (5) and L is the lateral side (13)
π·5·13=65π
Total: We add the total SA of the cylinder and cone together to find the total: 145π+65π = 210π cm²