Can I use 1 ml syringe for home insemination for pregnancy? What are my chance of getting pregnant if I inject sperm 5 days after my period?

Dangerous. It is not safe to do home insemination. The sperm needs to be "washed" and professionally prepared. Inflammatory reactions can occur in some cases. IUI with a fertility specialists usually run between $300-600 in most cases. Compared to the cost of raising a child or the cost of being treated in the ER after a problem this is a quite economical.
Here are some ... With today's American standard, it's absolutely not advisable to do what you described to enhance the odd to conceive. Remember ovulation (fertile time) takes place some 2 weeks before the period. Starting insemination 1-2 days before and onward for 3-4 days provides the prime opportunity to conceive if all the functional/anatomical state of all involved genital tracts is sound and well.