5 days is not too late for a tetanus shot.
If you haven't had a tetanus shot at all or it's been at least 10 years since your last tetanus shot you should get a tetanus shot if you think you may get a tetanus infection or if you've been cut with something rusty or you stepped on a nail.
Tetanus is very serious and can kill you so you should get a tetanus shot even if it's been 5 days, although it's best to get a tetanus shot soon after the injury.
The recommendation for a tetanus shot is in children they should get four doses of DTaP (diphtheria, tetanus, and pertussis) vaccine at 2, 4, 6, and 15-18 months.
And a booster dose of Tdap (tetanus, diphtheria, and pertussis) at 11-12 years.
For adolescence adults the recommendation for tetanus shots are a booster dose of Td (tetanus and diphtheria) every 10 years after the last Tdap dose.
Additional tetanus shot booster doses may be needed if you have a deep or dirty wound, you are traveling to an area with high risk of tetanus or you are pregnant (a Tdap booster is recommended during the third trimester).
For adults over 65 years of age that have not received a tetanus booster in the past 10 years should get a new tetanus booster.
The tetanus vaccine is a very effective vaccine and can provide you with long lasting protection, although your immunity also wanes over time, so you need regular tetanus boosters to maintain adequate protection against tetanus.