If we consider that m1 is the mass of the first object and a1 is the acceleration due to the application of an external force of 5N, from Newton’s 2nd law, we’ll have

For mass m1

newton 2nd law

F = m1a1

5 = m1×10

m1 = 21kg

For mass m2

F = m2a2

5 = m2 × 20

m2 = 1/4kg

if tied together

Total mass =m1+m2 =1/2 + 1/4 = 3/4kg

Now

F=MTQT

aT = 5/MT =5×4/3

=20/3 m/s2