Inclusion Criteria
* Subjects fully understand and voluntarily participate in this study and sign informed consent;
* Left Ventricular Ejection Fraction (LVEF) ≥ 50% within 28 days prior to first dose
* Eastern Cooperative Oncology Group performance status( PS) of 0 or 1.
* Life expectancy ≥ 3 months;
* During the screening period, the patients should meet the following requirements: Absolute value of neutrophils ≥ 1.5 × 109/L, Platelet ≥ 100 × 109/L, Hemoglobin ≥ 90 g/L (no blood transfusions and no use of CSF in 2 weeks); The internationally standardized ratio (INR), prothrombin time (PT) and activated partial thrombin time (APTT) ≤1.5 × ULN; Serum total bilirubin ≤ 1.5 × upper limit of normal (ULN); Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤ 3 × ULN, AST/ALT ≤ 5 × ULN for liver metastasis; Serum creatinine≤ 1.5×ULN，or Ccr ≥60 mL/min calculated by Cockcroft and Gault formula;
* Preferential subjects with measurable lesion in Part 1. and subjects with at least one measurable lesion in Part 2;
* All acute toxicity of previous anti-tumor treatment or surgery is relieved to baseline severity or NCI CTCAE version 5.0 ≤ 1;
* Eligible fertile female participants or male participants with fertile female sexual partners must agree to use an effective method of contraception from the study initiation until at least 6 months after the last treatment; Female participants of childbearing potential must have a negative serum pregnancy test within 7 days prior to enrollment.
* Histopathologically or cytologically confirmed advanced/unresectable or metastatic solid malignant tumors that is refractory to or intolerable with standard treatment, or for which no standard treatment is available in Part 1;
* Pathologically confirmed advanced/unresectable or metastatic breast cancer with HER2 overexpression that failed with one or more prior HER2 targeted therapy in Cohort A of Part 2;
* Pathologically confirmed advanced/unresectable or metastatic gastric or gastroesophageal junction adenocarcinoma with HER2 overexpression that failed with two or more prior HER2 targeted therapy in Cohort B of Part 2.
Exclusion Criteria
* A treatment history of antibody-drug conjugate containing topoisomerase I inhibitors;
* Subjects with one of the following conditions prior to first dose, including, but not limiting to：A major operation or severe trauma history within 4 weeks; A history of chemotherapy, targeted therapy, anti-angiogenesis therapy, biotherapy, immunotherapy, radiotherapy or other anti-tumor therapy within 4 weeks; A history of endocrine therapy within 3 weeks; A history of autologous stem cell transplant within 3 months;
* Subjects with other malignant tumors in the past three years (not including cured non-melanoma skin basal cell carcinoma, cervical carcinoma in situ and other malignancies of low malignant potential that have been effectively controlled without treatment);
* Subjects with symptomatic CNS metastasis (for example, cerebral edema requiring glucocorticoids therapy, or progressive CNS metastasis), not including prior cerebral and meningeal metastasis that is confirmed stable with MRI and without systematic glucocorticoids therapy；
* Adverse reactions from the previous anti-tumor treatment have not yet recovered (\>Grade 2 in NCI-CTCAE 5.0, with exception of alopecia and pigmentation or other adverse reactions judged no safety risk by the investigator);
* Subjects with clinically significant cardiovascular or cerebrovascular disease, including, but not limiting to: a medical history of symptomatic Congestive Heart Failure (CHF) (NYHA classes II-IV) or serious cardiac arrhythmia; a medical history of myocardial infarction or unstable angina within 6 months prior to screening; a QTc prolongation to \> 450 millisecond (ms) in males and \> 470 ms in females.
* Subjects with a medical history of interstitial lung disease (ILD)/pneumonia in need of glucocorticoids intervention，or with interstitial lung disease, or suspicious ILD by imaging detection at screening;
* Subjects with any uncontrolled active infection within 1 week prior to first dose;
* Subjects with positive human immunodeficiency virus (HIV) antibody, active hepatitis C (antibody positive with HCV RNA positive), active hepatitis B (positive hepatitis B virus surface antigen with HBV-DNA titer higher than the upper limit of the reference range);
* Subjects with concomitant disease potentially increasing toxicological risk；
* Known allergy to protein preparation or any protein drug with similar structure to FDA022-BB05;
* Subjects with a History of alcohol abuse or psychotropic/narcotic drug abuse;
* Pregnant or lactating women;
* Subjects with poor compliance, or not suitable for this study as determined by the investigator due to other reasons.
