The integrand is correct

However, the limits for r are 0 to 5.

To sweep out the disk r varies from the origin to the edge and then as theta varies from o to 2pi the entire disk is swept out.

A technical point

since you are regartding the thickness as negligible the density

shoud be 10gm/cm^2 otherwise you final result would be in gms/cm obviously not what you want