(2y + 5)²  + y²  =  5      simplify
4y² + 20y + 25 + y²  = 5
5y² + 20y +20  = 0      divide through by 5
y² + 4y + 4  =  0      factor
(y + 2)²  = 0        take the square root of both sides
y + 2   = 0
y  = -2
And x  = 2(-2) + 5   =  1
x=-4+5=1
x=1
Point of intersection = (1,-2)

Negative reciprocal gradient + touching at one point = tangent to circle.