Let a circle \( C \) of radius \( 5 \) lie below the \( x \)-axis. The line \( L_{1}: 4x+3y+2=0 \) passes through the centre \( P \) of the circle \( C \) and intersects line \( L_{2}: 3x-4y-11=0 \) at \( Q \). The line \( L_{2} \) touches \( C \) at the point \( Q \). Then the distance of \( P \) from the line \( 5x-12y+51=0 \) is ______.
