Diophantine equations

Hello, please help with sugesstions or solutions.

1. Are there integers x and y so valid: $x^2 -5xy +y^2 =3$ ?

2. Are there prime p and natural n so: $3p+1=k^3$ ?

3. Determine the naural numbers: $2<a<b<c<d<e$ so: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+ \frac{1}{d}+ \frac{1}{e} = 1$ .

Thank you for any help