is it fine if below 5 years babies play with pets or is it safe for them? bcz pets can have weird diseases...

Yes it's fine. I grew up with pets and me or any of my brothers had no health issues whatsoever. If you take care of pet, keep it clean, sterilised and make sure it is vaccinated every year -- there should be no problems with your kids playing with them. Pets are great for kids because taking care of them will teach compassion, responsibility, empathy and love for all of God's creations :)