Find the multiplicative inverse of $5$ in $\mathbb Z_{73}$

Question

I'm having some trouble with this question. The inverse should result in $44$ but I am getting $29$

$$73 = 14 \times 5 + 3$$

$$5 = 1 \times 3 + 2$$

$$3 = 1 \times 2 + 1$$

so $\gcd(73,5)=1$

using back substitution I then get:

$$1 = 3 - (2 \times 1)$$

$$1 = 3-(5 - (3 \times 1)) = 2(3)-5$$

$$1 = 2(73 - (14 \times 5)) - 5$$

$$1 = 2(73) - 29(5)$$

Answer 1

Observe $\,-29\equiv 44\mod73$.