My 5 weeks old baby is not feeding well , she does not show any sign of hunger and when she eventually does she only takes maximum 60ml per feeding which am forcing the bottle in her mouth to drink that much?

Needs a doctor visit: This is not normal. She may have a formula intolerance or milk protein allergy or reflux. She should be weighed to make sure she is gaining when she is taking so little. Most babies her age take 90 ml but I am more concerned that she does not seem hungry. She probably needs a specialty formula. She may also have tongue tie or lip tie preventing her from latching well.

Please have her see her doctor. Not feeding well can also be a sign of infection, in addition to Dr Gealow's answer.