Is it safe to cum inside 5 days after her period?

No. Pregnancy is known to have occurred from sex on any and all days of the cycle. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD.
Practice safe sex.
Get HPV vaccine,
Depends. On what you mean by safe. The risk of infection is low. Depending on how long her period is, you could be taking a chance at pregnancy however.