recall that s = rA where s is the arclength, r is the radius and A is the angle of the segment we're concerned with in radians (there's a different formula if you want to work in degrees).

=> A = s/r = 10/5 = 2 radians

now note that ABP forms an isoseles triangle, with base AB. we can find the length of AB using the Law of Cosines

AB^2 = AP^2 + BP^2 - 2AP*BPcosP

=> AB^2 = 5^2 + 5^2 - 2*5*5cos2 ....remember to put your calculator in radian mode

=> AB^2 = 50 - 50(-0.41615) = 70.8

=> AB = 8.41 approximately

I rounded off some when I was calculating so if you want a more "accurate" answer, redo the procedure with more decimal places

if you want to work in degrees, use the formula l = A/360 * 2pi*r where l is the arclength and A is the angle, and then use the Cosine rule for the length of the line once more (this time with your calculator in degrees mode).