sequences and series - $A=frac{6}{frac{6}{frac{6}{6-cdots}-5}-5}-5 :A=text{?}$

$$A=\cfrac 6 {\cfrac 6 {\cfrac 6 {6-\cdots}-5}-5}-5 :A=\text{?}$$
my try :

But I want to recurrence Sequence method!!

$$a_{n+1}=\frac{6}{a_n}-5: a_1=\text{?}$$

$$a_2=\frac 6 {a_1}-5,$$

$$a_3=\frac{6}{a_2}-5$$

???

thank you very much !