Let A(-5,1) divides the line joining (1,p) and (4,-2) in the ratio m:n

Then by section formula, x = (mx₂+nx₁)/(m+n)

-5 = (m×4+n×1)/(m+n)

-5 = (4m+n)/(m+n)

-5m-5n = 4m+n

-9m = 6n

m/n = -9/6 = -2/3 …(i)

By section formula, y = (my₂+ny₁)/(m+n)

1 = (m×-2+n×p)/(m+n)

1 = (-2m+pn)/(m+n)

m+n = -2m+pn

3m = (p-1)n

m/n = (p-1)/3 ….(ii)

Equating (i) and (ii)

(p-1)/3 = -2/3

p-1 = -2

p = -2+1 = -1

Hence the value of p is -1.