Given : A(a,3),B(2,1) and C(5,a) are collinear.
‌∴‌‌ Slope of ‌AB‌=‌ Slope of ‌BC
⇒‌‌

1−3

2−a

‌=‌

a−1

5−2

⇒‌‌

−2

2−a

‌=‌

a−1

3

⇒−6‌=(2−a)(a−1)
⇒−6‌=2a−2−a2+a
⇒‌a2−3a−4‌=0
⇒a2−4a+a−4‌=0
⇒‌(a−4)(a+1)‌=0
‌a‌=4,−1
Now equation of straight line are :
when a=4 ,
‌y−3=‌

1−3

2−4

(x−4)
‌y−3=‌

−2

−2

(x−4)
y−3‌=x−4
y‌=x−1
when a=−1,
y−3‌=‌

1−3

2+1

(x+1)
y−3‌=−‌

2

3

(x+1)
3y−9‌=−2x−2
3y+2x‌=7
Hence the equations of lines are
y=x−1‌ and ‌3y+2x=7