Periodic Fever Syndrome: This condition is characterized by recurring episodes of fever, often with a regular periodicity, which could fit the pattern of fevers every 5 days. Given the patient's history of Crohn's disease, an inflammatory bowel disease, and the absence of current flare, a periodic fever syndrome could be a plausible explanation, especially considering the elevated alkaline phosphatase (all phos) and gamma-glutamyl transferase (GGT), which might indicate liver or bone involvement.

Intra-abdominal Abscess: Although the patient's Crohn's disease is not currently in a flare, the history of Crohn's increases the risk of developing intra-abdominal abscesses, which can cause recurring fevers. The elevated liver enzymes could be secondary to the abscess affecting liver function.
Cholangitis: Given the elevated GGT, which is a marker of biliary tract disease, cholangitis (inflammation of the bile duct) could be a cause of recurring fevers, especially if there's an underlying biliary tract issue related to the Crohn's disease.
Osteomyelitis: The elevated alkaline phosphatase could indicate bone involvement, and osteomyelitis (bone infection) can cause recurring fevers. This could be related to the Crohn's disease if there's an associated bone infection.

Lymphoma: Patients with a history of Crohn's disease have an increased risk of developing lymphoma. Lymphoma can cause recurring fevers (as part of the B symptoms) and elevated liver enzymes due to liver involvement.
Tuberculosis (TB): TB can cause recurring fevers and has a wide range of presentations, including gastrointestinal and hepatic involvement, which could explain the elevated liver enzymes. It's crucial not to miss TB due to its serious consequences if left untreated.
Endocarditis: Although less likely without specific cardiac risk factors or symptoms, endocarditis can cause recurring fevers and has a high mortality rate if not promptly diagnosed and treated.

Familial Mediterranean Fever (FMF): This is a genetic disorder that causes recurring episodes of fever and inflammation, often affecting the abdomen, chest, or joints. It's rare but could be considered, especially if there's a family history or if the patient is of Mediterranean descent.
Hyper-IgD Syndrome (HIDS): A rare genetic disorder characterized by recurring episodes of fever, often with abdominal pain, and elevated IgD levels. It's a diagnosis of exclusion and would require specific testing to confirm.
Adult-onset Still's Disease: A rare inflammatory disorder that can cause recurring fevers, joint pain, and rash, among other symptoms. It's a diagnosis of exclusion and would require a thorough evaluation to consider.