Chronic Kidney Disease (CKD): This is a common condition in older adults, and the presence of moderate blood and protein in the urine is consistent with CKD, especially given the negative culture result which makes an infectious cause less likely.

Nephrotic Syndrome: Characterized by heavy proteinuria, which could be suggested by the moderate protein in the urine, although the presence of blood is not typical. However, some forms like membranous nephropathy can present with hematuria.
IgA Nephropathy: A common cause of recurrent hematuria, especially if the hematuria is episodic and follows a respiratory or gastrointestinal infection, though the culture-negative result doesn't directly support this.
Medullary Sponge Kidney: Could cause hematuria due to the cystic changes in the kidneys, but proteinuria is less commonly a dominant feature.

Urinary Tract Cancer (e.g., Bladder or Renal Cancer): Although less common, these conditions can present with hematuria and sometimes proteinuria. Given the potential severity and need for early intervention, they should not be missed.
Vasculitis (e.g., ANCA-associated vasculitis): Conditions like granulomatosis with polyangiitis can cause renal involvement with hematuria and proteinuria. Early diagnosis is crucial due to the potential for severe kidney damage and systemic complications.
Goodpasture Syndrome: An autoimmune disease that can cause glomerulonephritis and pulmonary hemorrhage, presenting with hematuria and sometimes proteinuria. It's rare but critical to diagnose early due to its potential severity.

Alport Syndrome: A genetic disorder affecting the type IV collagen in the kidneys, leading to hematuria and progressive kidney disease. It's less likely in a new presentation at 60 years old but could be considered if there's a family history.
Thin Basement Membrane Nephropathy: A benign condition causing isolated hematuria due to a thinning of the glomerular basement membrane. Proteinuria is less common, making this a less likely diagnosis given the moderate proteinuria.
Lupus Nephritis: Part of systemic lupus erythematosus, which can cause a variety of renal manifestations including hematuria and proteinuria. However, other systemic symptoms would typically be present.