Hi Jasbir.
thanks for asking in Healthcare Magic.
Continuous diarrhea in a five month old baby needs immediate medical attention and you should consult your treating Dr immediately. The most common causes for infant diarrhea are 
Lactose intolerance or infections like Rota virus, amoebisis or 
giardiasis. Infectious diarrhea is usually painful and severe. 
Stool test will confirm the diagnosis. 
Look for signs of 
dehydration like dry and sunken eyes, reduced urine, fatigue and irritability. Give electrolyte solution like Paedialyte every 4 to 6 hours. Do not stop breast milk if it is  infective diarrhea. If you have started solid food then give bland diet like rice gruel, bread and banana. Anti amoebic drugs will cure amoebiasis and giardiasis. Rota virus infection is usually self limiting. 
Your daughter is having persistent diarrhea. Watery  diarrhea for more than 10 days is called persistent  diarrhea. This is most commonly due to Lactose intolerance  Please check if diarrhea is due to milk. Stool pH will be less than 5.5 due to the presence of un absorbed lactose indicating  
lactose malabsorption. Lactose free formula that is available commercially  which contains soya will be useful. 
Napkin rash, the rash you are talking about can occur due to infection or due to the harsh detergents used to wash the napkins. Keep the area dry and use soft napkins. 
Zinc oxide cream or 
Hydrocortisone ointment may be useful. Your treating Dr will know about these preparations.
I hope this is useful to you.