Easy Math

Assuming that when she turns southwest, that she goes directly southwest at a 45degree angle.
Also that when she turns East she goes directly east making another 45 degree angle.

Total distance North 5.25km
Total Distance SW 2.75km
Total Distance E 3.79km

Y = distance north above the point where she crossed her own path going east.
N = 5.25-Y = distance north before paths crossed.
X = distance she traveled east before crossing her northern path
E = 3.79-X = distance after she passed her northern path.
Z = Distance from Starting Point to End Point.

This gives us our first right triangle
A = 90° a = 2.75km
B = 45° b = y
C = 45° c = x

SinB=Opposite/Hypotenuse
Sin45= X/2.75
X=1.94
SinC=Opposite/Hypotenuse
Sin45=Y/2.75
Y=1.94

Solve for N and E
N = 3.31
E = 1.85

From here there are a few ways we could find Z. I chose to use Pythagoras's theorem.
a^2+b^2=c^2
For my purposes a=N and b=E
(3.31^2)+(1.85^2)=Z^2
Z = 3.79km

She was 3.79km away from where she started.
Hope this helped, good luck.
- Ivy